Question

Find the height of a pyramid with a volume of 960 in^3 if the base is a square with a side length of 12 in.

What is the height?

Volume= 960 in^3

Side length 12 in.


(please hurry, due later today!)

Answer 1

Answer:

$20 \textsf{ in}$

Step-by-step explanation:

To find the height of the pyramid, we can use the formula for the volume of a pyramid:

$\Large\boxed{\boxed{ \textsf{Volume} = \dfrac{1}{3} \times \textsf{base area} \times \textsf{height}}}$

Given:

• Volume = 960 in³
• Base side length = 12 in

Since the base is a square, its area is side length squared.

$\textsf{Base area} = (\textsf{side length})^2 \\\\= (12 \textsf{ in})^2 \\\\= 144 \textsf{ in}^2$

Now, we can use the formula for the volume of a pyramid to find the height:

$960 = \dfrac{1}{3} \times 144 \times \textsf{height}$

First, let's solve for the height without the fraction:

$\textsf{height} = \dfrac{960 \times 3}{144}$

$\textsf{height} = \dfrac{2880}{144}$

$\textsf{height} = 20 \textsf{ in}$

Therefore, the height of the pyramid is 20 in.