Radius - ACT Math
Card 0 of 522
A circle with an area of 13_π_ in2 is centered at point C. What is the circumference of this circle?
A circle with an area of 13_π_ in2 is centered at point C. What is the circumference of this circle?
The formula for the area of a circle is A = _πr_2.
We are given the area, and by substitution we know that 13_π_ = _πr_2.
We divide out the π and are left with 13 = _r_2.
We take the square root of r to find that r = √13.
We find the circumference of the circle with the formula C = 2_πr_.
We then plug in our values to find C = 2√13_π_.
The formula for the area of a circle is A = _πr_2.
We are given the area, and by substitution we know that 13_π_ = _πr_2.
We divide out the π and are left with 13 = _r_2.
We take the square root of r to find that r = √13.
We find the circumference of the circle with the formula C = 2_πr_.
We then plug in our values to find C = 2√13_π_.
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A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle?
A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle?
First you must draw the diagram. The diagonal of the rectangle is also the diameter of the circle. The diagonal is the hypotenuse of a multiple of 2 of a 3,4,5 triangle, and therefore is 10.
Circumference = π * diameter = 10_π_.
First you must draw the diagram. The diagonal of the rectangle is also the diameter of the circle. The diagonal is the hypotenuse of a multiple of 2 of a 3,4,5 triangle, and therefore is 10.
Circumference = π * diameter = 10_π_.
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Ashley has a square room in her apartment that measures 81 square feet. What is the circumference of the largest circular area rug that she can fit in the space?
Ashley has a square room in her apartment that measures 81 square feet. What is the circumference of the largest circular area rug that she can fit in the space?
In order to solve this question, first calculate the length of each side of the room.
The length of each side of the room is also equal to the length of the diameter of the largest circular rug that can fit in the room. Since 
, the circumference is simply
In order to solve this question, first calculate the length of each side of the room.
The length of each side of the room is also equal to the length of the diameter of the largest circular rug that can fit in the room. Since 
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A gardener wants to build a fence around their garden shown below. How many feet of fencing will they need, if the length of the rectangular side is 12 and the width is 8?
A gardener wants to build a fence around their garden shown below. How many feet of fencing will they need, if the length of the rectangular side is 12 and the width is 8?
The shape of the garden consists of a rectangle and two semi-circles. Since they are building a fence we need to find the perimeter. The perimeter of the length of the rectangle is 24. The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle. Since we have two semi-circles we can find the circumference of one whole circle with a radius of 4, which would be 8π.
The shape of the garden consists of a rectangle and two semi-circles. Since they are building a fence we need to find the perimeter. The perimeter of the length of the rectangle is 24. The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle. Since we have two semi-circles we can find the circumference of one whole circle with a radius of 4, which would be 8π.
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If a circle has an area of 
, what is the circumference of the circle?
If a circle has an area of
The formula for the area of a circle is πr2. For this particular circle, the area is 81π, so 81π = πr2. Divide both sides by π and we are left with r2=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.
The formula for the area of a circle is πr2. For this particular circle, the area is 81π, so 81π = πr2. Divide both sides by π and we are left with r2=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.
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A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?
A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?
If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.
If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.
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A circle has the equation below. What is the circumference of the circle?
(x – 2)2 + (y + 3)2 = 9
A circle has the equation below. What is the circumference of the circle?
(x – 2)2 + (y + 3)2 = 9
The radius is 3. Yielding a circumference of 
.
The radius is 3. Yielding a circumference of
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The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle?
The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle?
We first must calculate the distance between these two points. Recall that the distance formula is:√((x2 - x1)2 + (y2 - y1)2)
For us, it is therefore: √((4 - 2)2 + (6 - 5)2) = √((2)2 + (1)2) = √(4 + 1) = √5
If d = √5, the circumference of our circle is πd, or π√5.
We first must calculate the distance between these two points. Recall that the distance formula is:√((x2 - x1)2 + (y2 - y1)2)
For us, it is therefore: √((4 - 2)2 + (6 - 5)2) = √((2)2 + (1)2) = √(4 + 1) = √5
If d = √5, the circumference of our circle is πd, or π√5.
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What is the circumference of a cirle with a radius of seven?
Leave your answer in terms of 
.
What is the circumference of a cirle with a radius of seven?
Leave your answer in terms of
Plug the radius into the circumference formula:
Plug the radius into the circumference formula:
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What is the circumference of a circle with a radius of six ft? Leave your answer in terms of 
.
What is the circumference of a circle with a radius of six ft? Leave your answer in terms of
To find the circumference given the radius, simply double the radius and mulitply by 
.
Thus:
To find the circumference given the radius, simply double the radius and mulitply by
Thus:
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A circle has an area of 
. Using this information find the circumference of the circle.
A circle has an area of
To find the circumference of a circle we use the formula
.
In order to solve we must use the given area to find the radius. Area of a circle has a formula of
.
So we manipulate that formula to solve for the radius.
.
Then we plug in our given area.
.
Now we plug our radius into the circumference equation to get the final answer.
.
To find the circumference of a circle we use the formula
In order to solve we must use the given area to find the radius. Area of a circle has a formula of
So we manipulate that formula to solve for the radius.
Then we plug in our given area.
Now we plug our radius into the circumference equation to get the final answer.
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A circle has an area of 
. Using this information find the circumference of the circle.
A circle has an area of
To find the circumference of a circle we use the formula
.
In order to solve we must use the given area to find the radius. Area of a circle has a formula of
.
So we manipulate that formula to solve for the radius.
.
Then we plug in our given area.
.
Now we plug our radius into the circumference equation to get the final answer.
.
To find the circumference of a circle we use the formula
In order to solve we must use the given area to find the radius. Area of a circle has a formula of
So we manipulate that formula to solve for the radius.
Then we plug in our given area.
Now we plug our radius into the circumference equation to get the final answer.
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A running track can be formed by adding a semicircle to each of the short ends of a rectangle of dimension 
.
If Tracy runs one lap around the track described above, how far has she run?
A running track can be formed by adding a semicircle to each of the short ends of a rectangle of dimension
If Tracy runs one lap around the track described above, how far has she run?
The questions really asks us to find the perimeter of the track.This would be the two long sides of the rectangle plus the circumferences of each of the two semicircles.
Each long side of the triangle is 
.
Each semicircle has a circumference that is 
because the whole circumference is
thus the semicircle circumference would be half of that or,
and 
.
Since the diameter of the semicircle is equal to the width of the rectangle, 
. That means each semicircle has a circumference of 
. Since we have two semicircles on the track, we can sum the two semicircle circumferences and the two long sides of the rectangle that comprise the track to get 
.
The questions really asks us to find the perimeter of the track.This would be the two long sides of the rectangle plus the circumferences of each of the two semicircles.
Each long side of the triangle is
Each semicircle has a circumference that is
Since the diameter of the semicircle is equal to the width of the rectangle,
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Find the circumference of a circle with radius 6.
Find the circumference of a circle with radius 6.
To solve, simply use the formula for the circumference of a circle.
In this particular case the radius of 6 should be substituted into the following equation to solve for the circumference.
Thus,
To solve, simply use the formula for the circumference of a circle.
In this particular case the radius of 6 should be substituted into the following equation to solve for the circumference.
Thus,
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A square with a side length of 4 inches is inscribed in a circle, as shown below. What is the area of the unshaded region inside of the circle, in square inches?
A square with a side length of 4 inches is inscribed in a circle, as shown below. What is the area of the unshaded region inside of the circle, in square inches?
Using the Pythagorean Theorem, the diameter of the circle (also the diagonal of the square) can be found to be 4√2. Thus, the radius of the circle is half of the diameter, or 2√2. The area of the circle is then π(2√2)2, which equals 8π. Next, the area of the square must be subtracted from the entire circle, yielding an area of 8π-16 square inches.
Using the Pythagorean Theorem, the diameter of the circle (also the diagonal of the square) can be found to be 4√2. Thus, the radius of the circle is half of the diameter, or 2√2. The area of the circle is then π(2√2)2, which equals 8π. Next, the area of the square must be subtracted from the entire circle, yielding an area of 8π-16 square inches.
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If a circle has a circumference of 16π, what would its area be if its radius were halved?
If a circle has a circumference of 16π, what would its area be if its radius were halved?
The circumference of a circle = πd where d = diameter. Therefore, this circle’s diameter must equal 16. Knowing that diameter = 2 times the radius, we can determine that the radius of this circle = 8. Halving the radius would give us a new radius of 4. To find the area of this new circle, use the formula A=πr² where r = radius. Plug in 4 for r. Area will equal 16π.
The circumference of a circle = πd where d = diameter. Therefore, this circle’s diameter must equal 16. Knowing that diameter = 2 times the radius, we can determine that the radius of this circle = 8. Halving the radius would give us a new radius of 4. To find the area of this new circle, use the formula A=πr² where r = radius. Plug in 4 for r. Area will equal 16π.
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Kate has a ring-shaped lawn which has an inner radius of 10 feet and an outer radius 25 feet. What is the area of her lawn?
Kate has a ring-shaped lawn which has an inner radius of 10 feet and an outer radius 25 feet. What is the area of her lawn?
The area of an annulus is
where 
is the radius of the larger circle, and 
is the radius of the smaller circle.
The area of an annulus is
where
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A star is inscribed in a circle with a diameter of 30, given the area of the star is 345, find the area of the shaded region, rounded to one decimal.
A star is inscribed in a circle with a diameter of 30, given the area of the star is 345, find the area of the shaded region, rounded to one decimal.
The area of the circle is (30/2)2*3.14 (π) = 706.5, since the shaded region is simply the area difference between the circle and the star, it’s 706.5-345 = 361.5
The area of the circle is (30/2)2*3.14 (π) = 706.5, since the shaded region is simply the area difference between the circle and the star, it’s 706.5-345 = 361.5
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If a circle has circumference 
, what is its area?
If a circle has circumference 
If the circumference is 
, then since 
we know 
. We further know that 
, so 
If the circumference is 
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The diameter of a circle increases by 100 percent. If the original area is 16π, what is the new area of the circle?
The diameter of a circle increases by 100 percent. If the original area is 16π, what is the new area of the circle?
The original radius would be 4, making the new radius 8 and by the area of a circle (A=π(r)2) the new area would be 64π.
The original radius would be 4, making the new radius 8 and by the area of a circle (A=π(r)2) the new area would be 64π.
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