Cones - Math

Card 1 of 244

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

You have an empty cylinder with a base diameter of 6 and a height of 10 and you have a cone full of water with a base radius of 3 and a height of 10. If you empty the cone of water into the cylinder, how much volume is left empty in the cylinder?

Tap to reveal answer

Answer

Cylinder Volume =

Cone Volume =

Cylinder Diameter = 6, therefore Cylinder Radius = 3

Cone Radius = 3

Empty Volume = Cylinder Volume – Cone Volume

$=\pi90-\pi30$

$=\pi*60$

← Didn't Know|Knew It →

Question

What is the volume of a right cone with a diameter of 6 cm and a height of 5 cm?

Tap to reveal answer

Answer

The general formula is given by V = 1/3Bh = 1/3pi $r^{2}$h, where = radius and = height.

The diameter is 6 cm, so the radius is 3 cm.

$V=\frac{\pi $3^2$\times 5}{3}$=15\pi$

← Didn't Know|Knew It →

Question

There is a large cone with a radius of 4 meters and height of 18 meters. You can fill the cone with water at a rate of 3 cubic meters every 25 seconds. How long will it take you to fill the cone?

Tap to reveal answer

Answer

First we will calculate the volume of the cone

$V=\frac{1}{3}$\pi $r^{2}$h=\frac{1}{3}$\pi\cdot $4^{2}$\cdot 18=96\pi\ $m^{3}$$

Next we will determine the time it will take to fill that volume

$96\pi \ $m^{3}$\times $\frac{25\ s}{3\ $m^{3}$$}=800\pi \ s$

We will then convert that into minutes

$800\pi \ s\times $\frac{1\ minute}{60\ seconds}$=13.$\overline{3}$\pi \ minutes\approx 41.9\ minutes\approx 41\ minutes\ 53\ seconds$

← Didn't Know|Knew It →

Question

What is the volume of a cone with a height of and a base with a radius of ?

Tap to reveal answer

Answer

To find the volume of a cone we must use the equation . In this formula, is the area of the circular base of the cone, and is the height of the cone.

We must first solve for the area of the base using .

The equation for the area of a circle is . Using this, we can adjust our formula and plug in the value of our radius.

$V=\frac{1}{3}$(169\pi)(H)$

Now we can plug in our given height, .

$V=\frac{1}{3}$(169\pi)(9)$

Multiply everything out to solve for the volume.

$V=\frac{1}{3}$(169\pi)(9)=(169\pi)(3)=507\pi$

The volume of the cone is $507\pi$ .

← Didn't Know|Knew It →

Question

What is the equation of a circle with a center of (5,15) and a radius of 7?

Tap to reveal answer

Answer

To find the equation of a circle we must first know the standard form of the equation of a circle which is

The letters and represent the -value and -value of the center of the circle respectively.

In this case is 5 and k is 15 so plugging the values into the equation yields

We then plug the radius into the equation to get

Square it to yield

The equation with a center of (5,15) and a radius of 7 is .

← Didn't Know|Knew It →

Question

What is the volume of a cone with base radius 4, and height 6?

Tap to reveal answer

Answer

The volume of a cone is , where is the height of the cone and is the base radius.

The volume of this cone is thus:

= $\frac{96\pi}{3}$

← Didn't Know|Knew It →

Question

$\textup{Find the volume, to the nearest cubic inch, of a cone with a radius of 8 inches}$

$\textup{at its base and a height of one foot.}$

Tap to reveal answer

Answer

$V= $\frac{1}{3}$ \pi $r^{2}$h;;\textup{Given: }r=8\textup{ inches}, h=12\textup{ inches}$

$V = $\frac{1}{3}$ $\pi\times8^{2}$\times12;;;;;V = 256\pi;;;V=804.2$

← Didn't Know|Knew It →

Question

What is the volume of a cone that has a radius of 3 and a height of 4?

Tap to reveal answer

Answer

The standard equation for the volume of a cone is

$v=\frac{1}{3}$\pi $(r)^2h$$

where denotes the radius and denotes the height.

Plug in the given values for and to find the answer:

$v=\frac{1}{3}$\pi $(3)^2$(4)=\frac{1}{3}$\pi (9)(4)=12\pi$

← Didn't Know|Knew It →

Question

Find the volume of the following cone.

Tap to reveal answer

Answer

The formula for the volume of a cone is:

$V= $\frac{\pi $r^{2}$$h}{3}$

where is the radius of the cone and is the height of the cone.

In order to find the height of the cone, use the Pythagorean Theorem:

Plugging in our values, we get:

$V= $\frac{\pi $(5m)^2$ (12m)}{3}$$

$V= \pi $(25m^2$)(4m)=100 \pi $m^3$$

← Didn't Know|Knew It →

Question

Find the volume of the following cone.

Tap to reveal answer

Answer

The formula for the volume of a cone is:

$V = $\frac{\pi $r^2$ h}{3}$$

Where is the radius of the cone and is the height of the cone

Use the Pythagorean Theorem to find the length of the radius:

Plugging in our values, we get:

$V = $\frac{\pi $(6m)^2$ 8m}{3}$$

$V = 96 \pi $m^3$$

← Didn't Know|Knew It →

Question

Find the volume of the following half cone.

Tap to reveal answer

Answer

The formula of the volume of a half cone is:

$V=\frac{1}{3}$(base)(height)$

$V = $\frac{1}{3}$\left($\frac{1}{2}$\pi $r^2$\right)(h)$

Where is the radius of the cone and is the height of the cone.

Use the Pythagorean Theorem to find the height of the cone:

$V = $\frac{1}{3}$\left($\frac{1}{2}$\pi $(8m)^2$\right)(15m)$

$V=160 \pi $m^3$$

← Didn't Know|Knew It →

Question

You have an empty cylinder with a base diameter of 6 and a height of 10 and you have a cone full of water with a base radius of 3 and a height of 10. If you empty the cone of water into the cylinder, how much volume is left empty in the cylinder?

Tap to reveal answer

Answer

Cylinder Volume =

Cone Volume =

Cylinder Diameter = 6, therefore Cylinder Radius = 3

Cone Radius = 3

Empty Volume = Cylinder Volume – Cone Volume

$=\pi90-\pi30$

$=\pi*60$

← Didn't Know|Knew It →

Question

What is the volume of a right cone with a diameter of 6 cm and a height of 5 cm?

Tap to reveal answer

Answer

The general formula is given by V = 1/3Bh = 1/3pi $r^{2}$h, where = radius and = height.

The diameter is 6 cm, so the radius is 3 cm.

$V=\frac{\pi $3^2$\times 5}{3}$=15\pi$

← Didn't Know|Knew It →

Question

There is a large cone with a radius of 4 meters and height of 18 meters. You can fill the cone with water at a rate of 3 cubic meters every 25 seconds. How long will it take you to fill the cone?

Tap to reveal answer

Answer

First we will calculate the volume of the cone

$V=\frac{1}{3}$\pi $r^{2}$h=\frac{1}{3}$\pi\cdot $4^{2}$\cdot 18=96\pi\ $m^{3}$$

Next we will determine the time it will take to fill that volume

$96\pi \ $m^{3}$\times $\frac{25\ s}{3\ $m^{3}$$}=800\pi \ s$

We will then convert that into minutes

$800\pi \ s\times $\frac{1\ minute}{60\ seconds}$=13.$\overline{3}$\pi \ minutes\approx 41.9\ minutes\approx 41\ minutes\ 53\ seconds$

← Didn't Know|Knew It →

Question

What is the volume of a cone with a height of and a base with a radius of ?

Tap to reveal answer

Answer

To find the volume of a cone we must use the equation . In this formula, is the area of the circular base of the cone, and is the height of the cone.

We must first solve for the area of the base using .

The equation for the area of a circle is . Using this, we can adjust our formula and plug in the value of our radius.

$V=\frac{1}{3}$(169\pi)(H)$

Now we can plug in our given height, .

$V=\frac{1}{3}$(169\pi)(9)$

Multiply everything out to solve for the volume.

$V=\frac{1}{3}$(169\pi)(9)=(169\pi)(3)=507\pi$

The volume of the cone is $507\pi$ .

← Didn't Know|Knew It →

Question

What is the equation of a circle with a center of (5,15) and a radius of 7?

Tap to reveal answer

Answer

To find the equation of a circle we must first know the standard form of the equation of a circle which is

The letters and represent the -value and -value of the center of the circle respectively.

In this case is 5 and k is 15 so plugging the values into the equation yields

We then plug the radius into the equation to get

Square it to yield

The equation with a center of (5,15) and a radius of 7 is .

← Didn't Know|Knew It →

Question

What is the volume of a cone with base radius 4, and height 6?

Tap to reveal answer

Answer

The volume of a cone is , where is the height of the cone and is the base radius.

The volume of this cone is thus:

= $\frac{96\pi}{3}$

← Didn't Know|Knew It →

Question

$\textup{Find the volume, to the nearest cubic inch, of a cone with a radius of 8 inches}$

$\textup{at its base and a height of one foot.}$

Tap to reveal answer

Answer

$V= $\frac{1}{3}$ \pi $r^{2}$h;;\textup{Given: }r=8\textup{ inches}, h=12\textup{ inches}$

$V = $\frac{1}{3}$ $\pi\times8^{2}$\times12;;;;;V = 256\pi;;;V=804.2$

← Didn't Know|Knew It →

Question

What is the volume of a cone that has a radius of 3 and a height of 4?

Tap to reveal answer

Answer

The standard equation for the volume of a cone is

$v=\frac{1}{3}$\pi $(r)^2h$$

where denotes the radius and denotes the height.

Plug in the given values for and to find the answer:

$v=\frac{1}{3}$\pi $(3)^2$(4)=\frac{1}{3}$\pi (9)(4)=12\pi$

← Didn't Know|Knew It →

Question

Find the volume of the following cone.

Tap to reveal answer

Answer

The formula for the volume of a cone is:

$V= $\frac{\pi $r^{2}$$h}{3}$

where is the radius of the cone and is the height of the cone.

In order to find the height of the cone, use the Pythagorean Theorem:

Plugging in our values, we get:

$V= $\frac{\pi $(5m)^2$ (12m)}{3}$$

$V= \pi $(25m^2$)(4m)=100 \pi $m^3$$

← Didn't Know|Knew It →

0

Knew It