HSPT Math - How to find the volume of a figure

What is the volume of a cylinder with a diameter of 13 inches and a height of 27.5 inches?

$381.44\pi \ in^{3}$

$2583.1\pi \ in^{3}$

$357.5\pi \ in^{3}$

$4647.5\ in^{3}$

$1161.88\pi \ in^{3}$

Explanation

The equation for the volume of a cylinder is V = Ah, where A is the area of the base and h is the height.

Thus, the volume can also be expressed as V = πr2h.

The diameter is 13 inches, so the radius is 13/2 = 6.5 inches.

Now we can easily calculate the volume:

V = 6.52π * 27.5 = 1161.88π in3

What is the volume of the rectangular prism below?

Screen shot 2015 11 05 at 1.03.11 pm

Explanation

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=5\times\5\times6$

$\small v=150cm^3$

Remember, volume is always labeled as units to the third power.

Cylinder

The volume of the above cylinder is 80% of what number?

$45,000 \pi$

$28,000 \pi$

$1,680 \pi$

$2,625 \pi$

Explanation

The volume of the cylinder can be calculated by setting and in the formula

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

$V = \pi \cdot 30 ^{2} \cdot 40$

$V = \pi \cdot 900 \cdot 40$

$V =36,000 \pi$

This is 80% of the number

$36,000 \pi \div \frac{80}{100} = 36,000 \pi \cdot \frac{100} {80}= 45,000 \pi$

Prism

Give the volume of the above box in cubic centimeters.

$324,000 \textrm{ cm}^{3}$

$32,400 \textrm{ cm}^{3}$

$21,600\textrm{ cm}^{3}$

$28,800 \textrm{ cm}^{3}$

$216,000 \textrm{ cm}^{3}$

Explanation

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

$0.9 \times 100 = 90$ centimeters

$0.6 \times 100 = 60$ centimeters

Use the volume formula, substituting :

$V = 90 \cdot 60 \cdot 60 = 324,000$ cubic centimeters

A foam ball has a volume of 2 units and has a diameter of x. If a second foam ball has a radius of 2x, what is its volume?

128 units

16 units

8 units

4 units

2 units

Explanation

Careful not to mix up radius and diameter. First, we need to identify that the second ball has a radius that is 4 times as large as the first ball. The radius of the first ball is (1/2)x and the radius of the second ball is 2x. The volume of the second ball will be 43, or 64 times bigger than the first ball. So the second ball has a volume of 2 * 64 = 128.

Claire's cylindrical water bottle is 9 inches tall and has a diameter of 6 inches. How many cubic inches of water will her bottle hold?

$81\pi$

$324\pi$

$54\pi$

$18\pi$

$45\pi$

Explanation

The volume is the area of the base times the height. The area of the base is $\pi r^{2}$ , and the radius here is 3. $\pi\cdot 3^{2}\cdot 9=81\pi$

Chemicals to clean a swimming pool cost $0.24 per cubic foot of water. If a pool is 6 feet deep, 14 feet long and 8 feet wide, how much does it cost to clean the pool? Round to the nearest dollar.

Explanation

The volume of the pool can be determined by multiplying the length, width, and height together.

$V = 6 \times 8 \times 14 = 672 ft^{3}$

Each cubit foot costs 24 cents, so:

$672ft^3\times $0.24=$161.28\approx $161$

A hollow prism has a base 12 in x 13 in and a height of 42 in. A closed, cylindrical can is placed in the prism. The remainder of the prism is then filled with gel, surrounding the can. The thickness of the can is negligible. Its diameter is 9 in and its height is one-fourth that of the prism. The can has a mass of 1.5 g per in3, and the gel has a mass of 2.2 g per in3. What is the approximate overall mass of the contents of the prism?

15.22 kg

139.44 g

973.44 g

11.48 kg

13.95 kg

Explanation

We must find both the can volume and the gel volume. The formula for the gel volume is:

Gel volume = Prism volume – Can volume

The prism volume is simple: 12 * 13 * 42 = 6552 in3

The volume of the can is found by multiplying the area of the circular base by the height of the can. The height is one-fourth the prism height, or 42/4 = 10.5 in. The area of the base is equal to πr_2. Note that the prompt has given the diameter. Therefore, the radius is 4.5, not 9. The base's area is: 4.52_π = 20.25_π_. The total volume is therefore: 20.25_π_ * 10.5 = 212.625_π_ in3.

The gel volume is therefore: 6552 – 212.625_π_ or (approx.) 5884.02 in3.

The approximate volume for the can is: 667.98 in3

From this, we can calculate the approximate mass of the contents:

Gel Mass = Gel Volume * 2.2 = 5884.02 * 2.2 = 12944.844 g

Can Mass = Can Volume * 1.5 = 667.98 * 1.5 = 1001.97 g

The total mass is therefore 12944.844 + 1001.97 = 13946.814 g, or approximately 13.95 kg.

What is the volume of the rectangular prism below?

Screen shot 2015 11 05 at 1.35.53 pm