GED Math - Volume of Other Solids

Find the volume of a cube with a width of 11in.

$1331\text{in}^3$

$1111\text{in}^3$

$1221\text{in}^3$

$1121\text{in}^3$

$1212\text{in}^3$

Explanation

To find the volume of a cube, we will use the following formula:

$V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height of the cube.

Now, we know the width of the cube is 11in. Because it is a cube, all widths/lengths/etc are the same. Therefore, the length and the height are also 11in. So, we substitute. We get

$V = 11\text{in} \cdot 11\text{in} \cdot 11\text{in}$

$V = 121\text{in}^2 \cdot 11\text{in}$

$V = 1331\text{in}^3$

Find the volume of a cone with a radius of $6\pi$ and a height of .

$24 \pi ^3$

$12\pi^2$

$48 \pi ^3$

$24 \pi ^2$

$48 \pi ^4$

Explanation

Write the formula for the volume of a cone.

$V = \frac{1}{3}\pi r^2h$

Substitute the radius and height into the formula.

$V = \frac{1}{3}\pi (6\pi)^2(2) = \frac{1}{3}\pi (6\pi)(6\pi)(2)$

The answer is: $24 \pi ^3$

Let $\pi = 3.14$ .

A cone has a height of 5in and a diameter of 12in. Find the volume.

$188.4\text{in}^3$

$94.20\text{in}^3$

$471\text{in}^3$

$376.80\text{in}^3$

$452.16\text{in}^3$

Explanation

To find the volume of a cone, we will use the following formula:

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

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

We know $\pi=3.14$ .

We know the diameter of the cone is 12in. We know the diameter is two times the radius. So, the radius is 6in.

We know the height is 5in.

Now, we can substitute. We get

$V = 3.14 \cdot (6\text{in})^2 \cdot \frac{5\text{in}}{3}$

$V = 3.14 \cdot 36\text{in}^2 \cdot \frac{5\text{in}}{3}$

Now, we can simplify to make things easier. The 36 and the 3 can both be divided by 3. So, we get

$V = 3.14 \cdot 12\text{in}^2 \cdot \frac{5\text{in}}{1}$

$V = 3.14 \cdot 12\text{in}^2 \cdot 5\text{in}$

$V = 3.14 \cdot 60\text{in}^3$

$V = 188.4\text{in}^3$

A cube has a length of 9cm. Find the volume.

$729\text{cm}^3$

$81\text{cm}^3$

$486\text{cm}^3$

$381\text{cm}^3$

$567\text{cm}^3$

Explanation

To find the volume of a cube, we will use the following formula:

$V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height of the cube.

Now, we know the length of the cube is 9cm. Because it is a cube, all sides/lengths are equal. Therefore, the width and height are also 9cm.

Knowing this, we can substitute into the formula. We get

$V = 9\text{cm} \cdot 9\text{cm} \cdot 9\text{cm}$

$V = 81\text{cm}^2 \cdot 9\text{cm}$

$V = 729\text{cm}^3$

Find the volume of a cone with a radius of 8in and a height of 6in.

$128\pi \text{ in}^3$

$48\pi \text{ in}^3$

$384\pi \text{ in}^3$

$144\pi \text{ in}^3$

$96\pi \text{ in}^3$

Explanation

To find the volume of a cone, we will use the following formula:

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

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

Now, we know the radius is 8in. We know the height is 6in. So, we can substitute. We get

$V = \pi \cdot (8\text{in})^2 \cdot \frac{6\text{in}}{3}$

$V = \pi \cdot 64\text{in}^2 \cdot 2\text{in}$

$V = \pi \cdot 128\text{in}^3$

$V = 128\pi \text{ in}^3$

Find the volume of a cone with a radius of 2 and a height of 10.

$\frac{40}{3}\pi$

$\frac{20}{3}\pi$

$\frac{200}{3}\pi$

$\frac{100}{3}\pi$

$20\pi$

Explanation

Write the formula for the volume of a cone.

$V =\frac{1}{3}\pi r^2 h$

Substitute the radius and height.

$V =\frac{1}{3}\pi (2)^2 (10) = \frac{40}{3}\pi$

The answer is: $\frac{40}{3}\pi$

An office uses cone-shaped paper cups for water in their water cooler. The cups have a radius of inches and a height of inches. If the water cooler can hold cubic inches of water, how many complete cups of water can the water cooler fill?

Explanation

Start by finding the volume of a cup.

Recall how to find the volume of a cone:

$\text{Volume of Cone}=\frac{1}{3}\pi r^2 h$

Plug in the given radius and height to find the volume.

$\text{Volume}=\frac{1}{3}\pi(3)^2(4.25)=40.055$

Now divide the total volume of the water in the water cooler by the volume of one cup in order to find how many complete cups the water cooler can fill.

$\text{Number of cups filled}=\frac{1155}{40.055}=28.84$