How to find the volume of a pyramid in pre-algebra

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Math › How to find the volume of a pyramid in pre-algebra

Questions 1 - 6

1

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:

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

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

2

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:

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

3

What is the volume of a pyramid with a square base length of and a height of ?

Explanation

To find the volume of a pyramid we must use the equation

$V=\left ( \frac{1}{3} \right )\times Area\ of\ base\times height$

We must first solve for the area of the square using

We plug in and square it to get .

We then plug our answer into the equation for the volume of the pyramid

$V=\frac{1}{3}\cdot (25)\cdot (21)$

We multiply the result to get our final answer for the volume of the pyramid

4

What is the volume of a pyramid with a square base that has a side length of and a height of ?

Explanation

To find the volume of a pyramid we must use the equation

$V=\left(\frac{1}{3}\cdot \right)(Base\ Area)\cdot (Height)$

We must first solve for the area of the square using $A=s^{2}$

We plug in and square it to get $A=12^{2}$

We then plug our answer into the equation for the volume of the pyramid with

It will look like this

$V=\left(\frac{1}{3}\right)\cdot (144)\cdot (14)$

We multiply the result to get our final answer for the volume of the pyramid .

5

What is the volume of a square-based pyramid with side lengths and a height of ?

Explanation

To find the volume of a pyramid, use the equation:

$Volume=\frac{1}{3}(Base\ Area)(Height)$

First solve for the base area (which is a square) using $Base\ Area=Side^{2}$

$Base\ Area=8^{2}$

$Base\ Area=64$

Then subsitute the base area into the volume formula and obtain:

$Volume=(\frac{1}{3})(64)(21)$

6

What is the volume of a pyramid with a square side length of and a height of ?

Explanation

To find the volume of a pyramid we must use the equation $Volume:of:pyramid=\frac{1}{3}(Area: of: square)(height)$

We must first solve for the area of the square using $Area: of: square=(side: length)^{2}$

We plug in and square it to get $8^{2}=64$

We then plug our answer into the equation for the pyramid with $Volume:of:pyramid=\frac{1}{3}(64)(15)$

We multiply the result by $\frac{1}{3}$ to get our final answer for the volume of the pyramid .

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