Math - Volume of a Figure

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

$18\pi \ m^3$

$54\pi \ m^3$

$72\pi \ m^3$

$9\pi \ m^3$

$36\pi \ m^3$

Explanation

The formula for the volume of a cone is $\frac{1}{3}{\pi}r^{2}h$ .

Notice that we are given the diameter, meters, not the radius; thus, we have to solve for the radius by dividing the diameter by two. The radius is therefore 3 meters. Then, we plug this value into the formula for volume:

$\frac{1}{3}{\pi}(3)^{2}\cdot 6 = \frac{1}{3}{\pi}9\cdot 6 = 18{\pi}\ \textup{meters}^3=18\pi m^3$

What is the volume of a pyramid with a base area of 9 sqaure centimeters and a height of 4 centimeters?

$12\ cm^3$

$108\ cm^3$

$48\ cm^3$

$36\ cm^3$

Explanation

The volume of a pyramid can be determined using the following equation:

$V=\frac{1}{3}lwh=\frac{1}{3}Ah$

$V=\frac{1}{3}(9\ cm^2)(4cm)=\frac{1}{3}36\ cm^3=12\ cm^3$

What is the volume of a pyramid with a base area of 9 sqaure centimeters and a height of 4 centimeters?

$12\ cm^3$

$108\ cm^3$

$48\ cm^3$

$36\ cm^3$

Explanation

The volume of a pyramid can be determined using the following equation:

$V=\frac{1}{3}lwh=\frac{1}{3}Ah$

$V=\frac{1}{3}(9\ cm^2)(4cm)=\frac{1}{3}36\ cm^3=12\ cm^3$

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

$18\pi \ m^3$

$54\pi \ m^3$

$72\pi \ m^3$

$9\pi \ m^3$

$36\pi \ m^3$

Explanation

The formula for the volume of a cone is $\frac{1}{3}{\pi}r^{2}h$ .

$\frac{1}{3}{\pi}(3)^{2}\cdot 6 = \frac{1}{3}{\pi}9\cdot 6 = 18{\pi}\ \textup{meters}^3=18\pi m^3$

What is the volume of a sphere with a radius of ?

$36\pi$

$\frac{4}{3}\pi$

$9\pi$

$27\pi$

$81\pi$

Explanation

The formula for the volume of a sphere is $V=\frac{4}{3}\pi r^3$ .

Plug in our radius to solve:

$V=\frac{4}{3}\pi r^3$

$V=\frac{4}{3}\pi *3^3$

$V=\frac{4}{3}*\pi*27$

$V=36\pi$

A cylinder has a radius of inches and a height of inches. What is the volume of the cylinder?

$45\pi$ inches cubed

inches cubed

$15\pi$ inches cubed

inches cubed

Explanation

The formula for the volume of a cylinder is $V = \pi r^{2}h$ , where is the radius, and is the height.

Plugging into this formula with our given values, we see that $V = \pi (3)^{2}(5) = \pi (9)(5) = 45\pi$ inches cubed.

What is the volume of a sphere with a radius of ?

$36\pi$

$\frac{4}{3}\pi$

$9\pi$

$27\pi$

$81\pi$

Explanation

The formula for the volume of a sphere is $V=\frac{4}{3}\pi r^3$ .

Plug in our radius to solve:

$V=\frac{4}{3}\pi r^3$

$V=\frac{4}{3}\pi *3^3$

$V=\frac{4}{3}*\pi*27$

$V=36\pi$

What is the volume of a pyramid with a base length of 5 inches, base width of 6 inches, and height of 8 inches?

$80\ in^3$

$240\ in^3$

$120\ in^3$

$60\ in^3$

Explanation

The volume of a pyramid can be determined using the equation:

$V=\frac{1}{3}lwh=\frac{1}{3}(5\ in)(6\ in)(8\ in)=\frac{1}{3}240\ in^3=80\ in^3$

What is the volume of a pyramid with a base length of 5 inches, base width of 6 inches, and height of 8 inches?

$80\ in^3$

$240\ in^3$

$120\ in^3$

$60\ in^3$

Explanation

The volume of a pyramid can be determined using the equation:

$V=\frac{1}{3}lwh=\frac{1}{3}(5\ in)(6\ in)(8\ in)=\frac{1}{3}240\ in^3=80\ in^3$

A cylinder has a radius of inches and a height of inches. What is the volume of the cylinder?

$45\pi$ inches cubed

inches cubed

$15\pi$ inches cubed

inches cubed

Explanation

The formula for the volume of a cylinder is $V = \pi r^{2}h$ , where is the radius, and is the height.

Plugging into this formula with our given values, we see that $V = \pi (3)^{2}(5) = \pi (9)(5) = 45\pi$ inches cubed.

Volume of a Figure

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