How to find the length of an arc - ISEE Upper Level Quantitative Reasoning

Card 1 of 20

Didn't Know

Knew It

1 of 2019 left

Question

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?

Tap to reveal answer

Answer

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is $2\pi r = 2 \pi \times 3 = 6\pi$ feet. minutes is one-third of an hour, so the tip of the minute hand moves $$\frac{1}{3}$ \times 6\pi = 2\pi$ feet, or $2\pi \times 12 = 24\pi$ inches.

← Didn't Know|Knew It →

Question

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?

Tap to reveal answer

Answer

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is $2\pi r = 2 \pi \times 6 = 12\pi$ feet. One hour and twenty minutes is $1 $\frac{1}{3}$$ hours, so the tip of the hand moved $1 $\frac{1}{3}$ \times 12 \pi = 16 \pi$ feet, or $16 \pi \times 12 = 192 \pi$ inches.

← Didn't Know|Knew It →

Question

In the above figure, express in terms of .

Tap to reveal answer

Answer

The measure of an arc - $\overarc{AB}$ - intercepted by an inscribed angle - $\angle ACB$ - is twice the measure of that angle, so

$m \overarc{AB} = 2 \cdot m \angle ACB$

$\frac{4y}{4}$ = $\frac{4x- 27}{4}$

$y = x- $\frac{27}{4}$$

← Didn't Know|Knew It →

Question

In the above diagram, radius .

Give the length of $\overarc {AB}$ .

Tap to reveal answer

Answer

The circumference of a circle is $2 \pi$ multiplied by its radius , so

$C = 2 \pi \cdot OA = 2 \pi \cdot 12 = 24 \pi$ .

$\angle ACB$ , being an inscribed angle of the circle, intercepts an arc $\overarc {AB}$ with twice its measure:

$m \overarc {AB} = 2 \cdot m\angle ACB = 2 \cdot 72 ^{\circ } = 144 ^{\circ }$

The length of $\overarc {AB}$ is the circumference multiplied by $\frac{144}{360}$ :

$\frac{144}{360}$ \times 24 \pi = $\frac{48 \pi }{5}$ .

← Didn't Know|Knew It →

Question

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

Tap to reveal answer

Answer

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

To begin, let's recall our formula for length of an arc.

Now, just plug in and simplify

So, our answer is 4.54in

← Didn't Know|Knew It →

Question

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?

Tap to reveal answer

Answer

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is $2\pi r = 2 \pi \times 3 = 6\pi$ feet. minutes is one-third of an hour, so the tip of the minute hand moves $$\frac{1}{3}$ \times 6\pi = 2\pi$ feet, or $2\pi \times 12 = 24\pi$ inches.

← Didn't Know|Knew It →

Question

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?

Tap to reveal answer

Answer

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is $2\pi r = 2 \pi \times 6 = 12\pi$ feet. One hour and twenty minutes is $1 $\frac{1}{3}$$ hours, so the tip of the hand moved $1 $\frac{1}{3}$ \times 12 \pi = 16 \pi$ feet, or $16 \pi \times 12 = 192 \pi$ inches.

← Didn't Know|Knew It →

Question

In the above figure, express in terms of .

Tap to reveal answer

Answer

The measure of an arc - $\overarc{AB}$ - intercepted by an inscribed angle - $\angle ACB$ - is twice the measure of that angle, so

$m \overarc{AB} = 2 \cdot m \angle ACB$

$\frac{4y}{4}$ = $\frac{4x- 27}{4}$

$y = x- $\frac{27}{4}$$

← Didn't Know|Knew It →

Question

In the above diagram, radius .

Give the length of $\overarc {AB}$ .

Tap to reveal answer

Answer

The circumference of a circle is $2 \pi$ multiplied by its radius , so

$C = 2 \pi \cdot OA = 2 \pi \cdot 12 = 24 \pi$ .

$\angle ACB$ , being an inscribed angle of the circle, intercepts an arc $\overarc {AB}$ with twice its measure:

$m \overarc {AB} = 2 \cdot m\angle ACB = 2 \cdot 72 ^{\circ } = 144 ^{\circ }$

The length of $\overarc {AB}$ is the circumference multiplied by $\frac{144}{360}$ :

$\frac{144}{360}$ \times 24 \pi = $\frac{48 \pi }{5}$ .

← Didn't Know|Knew It →

Question

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

Tap to reveal answer

Answer

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

To begin, let's recall our formula for length of an arc.

Now, just plug in and simplify

So, our answer is 4.54in

← Didn't Know|Knew It →

Question

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?

Tap to reveal answer

Answer

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is $2\pi r = 2 \pi \times 3 = 6\pi$ feet. minutes is one-third of an hour, so the tip of the minute hand moves $$\frac{1}{3}$ \times 6\pi = 2\pi$ feet, or $2\pi \times 12 = 24\pi$ inches.

← Didn't Know|Knew It →

Question

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?

Tap to reveal answer

Answer

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is $2\pi r = 2 \pi \times 6 = 12\pi$ feet. One hour and twenty minutes is $1 $\frac{1}{3}$$ hours, so the tip of the hand moved $1 $\frac{1}{3}$ \times 12 \pi = 16 \pi$ feet, or $16 \pi \times 12 = 192 \pi$ inches.

← Didn't Know|Knew It →

Question

In the above figure, express in terms of .

Tap to reveal answer

Answer

The measure of an arc - $\overarc{AB}$ - intercepted by an inscribed angle - $\angle ACB$ - is twice the measure of that angle, so

$m \overarc{AB} = 2 \cdot m \angle ACB$

$\frac{4y}{4}$ = $\frac{4x- 27}{4}$

$y = x- $\frac{27}{4}$$

← Didn't Know|Knew It →

Question

In the above diagram, radius .

Give the length of $\overarc {AB}$ .

Tap to reveal answer

Answer

The circumference of a circle is $2 \pi$ multiplied by its radius , so

$C = 2 \pi \cdot OA = 2 \pi \cdot 12 = 24 \pi$ .

$\angle ACB$ , being an inscribed angle of the circle, intercepts an arc $\overarc {AB}$ with twice its measure:

$m \overarc {AB} = 2 \cdot m\angle ACB = 2 \cdot 72 ^{\circ } = 144 ^{\circ }$

The length of $\overarc {AB}$ is the circumference multiplied by $\frac{144}{360}$ :

$\frac{144}{360}$ \times 24 \pi = $\frac{48 \pi }{5}$ .

← Didn't Know|Knew It →

Question

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

Tap to reveal answer

Answer

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

To begin, let's recall our formula for length of an arc.

Now, just plug in and simplify

So, our answer is 4.54in

← Didn't Know|Knew It →

Question

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?

Tap to reveal answer

Answer

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is $2\pi r = 2 \pi \times 3 = 6\pi$ feet. minutes is one-third of an hour, so the tip of the minute hand moves $$\frac{1}{3}$ \times 6\pi = 2\pi$ feet, or $2\pi \times 12 = 24\pi$ inches.

← Didn't Know|Knew It →

Question

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?

Tap to reveal answer

Answer

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is $2\pi r = 2 \pi \times 6 = 12\pi$ feet. One hour and twenty minutes is $1 $\frac{1}{3}$$ hours, so the tip of the hand moved $1 $\frac{1}{3}$ \times 12 \pi = 16 \pi$ feet, or $16 \pi \times 12 = 192 \pi$ inches.

← Didn't Know|Knew It →

Question

In the above figure, express in terms of .

Tap to reveal answer

Answer

The measure of an arc - $\overarc{AB}$ - intercepted by an inscribed angle - $\angle ACB$ - is twice the measure of that angle, so

$m \overarc{AB} = 2 \cdot m \angle ACB$

$\frac{4y}{4}$ = $\frac{4x- 27}{4}$

$y = x- $\frac{27}{4}$$

← Didn't Know|Knew It →

Question

In the above diagram, radius .

Give the length of $\overarc {AB}$ .

Tap to reveal answer

Answer

The circumference of a circle is $2 \pi$ multiplied by its radius , so

$C = 2 \pi \cdot OA = 2 \pi \cdot 12 = 24 \pi$ .

$\angle ACB$ , being an inscribed angle of the circle, intercepts an arc $\overarc {AB}$ with twice its measure:

$m \overarc {AB} = 2 \cdot m\angle ACB = 2 \cdot 72 ^{\circ } = 144 ^{\circ }$

The length of $\overarc {AB}$ is the circumference multiplied by $\frac{144}{360}$ :

$\frac{144}{360}$ \times 24 \pi = $\frac{48 \pi }{5}$ .

← Didn't Know|Knew It →

Question

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

Tap to reveal answer

Answer

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

To begin, let's recall our formula for length of an arc.

Now, just plug in and simplify

So, our answer is 4.54in

← Didn't Know|Knew It →

Knew It

How to find the length of an arc - ISEE Upper Level Quantitative Reasoning

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is feet. minutes is one-third of an hour, so the tip of the minute hand moves feet, or inches.

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is feet. One hour and twenty minutes is hours, so the tip of the hand moved feet, or inches.

In the above figure, express in terms of .

The measure of an arc - - intercepted by an inscribed angle - - is twice the measure of that angle, so

In the above diagram, radius . Give the length of .

The circumference of a circle is multiplied by its radius , so . , being an inscribed angle of the circle, intercepts an arc with twice its measure: The length of is the circumference multiplied by : .

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is feet. minutes is one-third of an hour, so the tip of the minute hand moves feet, or inches.

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is feet. One hour and twenty minutes is hours, so the tip of the hand moved feet, or inches.

In the above figure, express in terms of .

The measure of an arc - - intercepted by an inscribed angle - - is twice the measure of that angle, so

In the above diagram, radius . Give the length of .

The circumference of a circle is multiplied by its radius , so . , being an inscribed angle of the circle, intercepts an arc with twice its measure: The length of is the circumference multiplied by : .

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is feet. minutes is one-third of an hour, so the tip of the minute hand moves feet, or inches.

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is feet. One hour and twenty minutes is hours, so the tip of the hand moved feet, or inches.

In the above figure, express in terms of .

The measure of an arc - - intercepted by an inscribed angle - - is twice the measure of that angle, so

In the above diagram, radius . Give the length of .

The circumference of a circle is multiplied by its radius , so . , being an inscribed angle of the circle, intercepts an arc with twice its measure: The length of is the circumference multiplied by : .

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is feet. minutes is one-third of an hour, so the tip of the minute hand moves feet, or inches.

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is feet. One hour and twenty minutes is hours, so the tip of the hand moved feet, or inches.

In the above figure, express in terms of .

The measure of an arc - - intercepted by an inscribed angle - - is twice the measure of that angle, so

In the above diagram, radius . Give the length of .

The circumference of a circle is multiplied by its radius , so . , being an inscribed angle of the circle, intercepts an arc with twice its measure: The length of is the circumference multiplied by : .

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

The measure of an arc - $\overarc{AB}$ - intercepted by an inscribed angle - $\angle ACB$ - is twice the measure of that angle, so

$m \overarc{AB} = 2 \cdot m \angle ACB$

$\frac{4y}{4}$ = $\frac{4x- 27}{4}$

$y = x- $\frac{27}{4}$$

In the above diagram, radius .

Give the length of $\overarc {AB}$ .

The measure of an arc - $\overarc{AB}$ - intercepted by an inscribed angle - $\angle ACB$ - is twice the measure of that angle, so

$m \overarc{AB} = 2 \cdot m \angle ACB$

$\frac{4y}{4}$ = $\frac{4x- 27}{4}$

$y = x- $\frac{27}{4}$$

In the above diagram, radius .

Give the length of $\overarc {AB}$ .

The measure of an arc - $\overarc{AB}$ - intercepted by an inscribed angle - $\angle ACB$ - is twice the measure of that angle, so

$m \overarc{AB} = 2 \cdot m \angle ACB$

$\frac{4y}{4}$ = $\frac{4x- 27}{4}$

$y = x- $\frac{27}{4}$$

In the above diagram, radius .

Give the length of $\overarc {AB}$ .

The measure of an arc - $\overarc{AB}$ - intercepted by an inscribed angle - $\angle ACB$ - is twice the measure of that angle, so

$m \overarc{AB} = 2 \cdot m \angle ACB$

$\frac{4y}{4}$ = $\frac{4x- 27}{4}$

$y = x- $\frac{27}{4}$$

In the above diagram, radius .

Give the length of $\overarc {AB}$ .