Question

A regular square pyramid has volume of 2400 centimeters cubed and height of 18 centimeters.

Question
Calculate the approximate base length of the pyramid.

Answer options with 5 options
A.
6.7 centimeters

B.
14.1 centimeters

C.
20.0 centimeters

D.
22.2 centimeters

E.
36.5 centimeters

Answer 1

To find the approximate base length of the regular square pyramid, we can use the formula for the volume of a pyramid:

\[
V = \frac{1}{3} \times B \times h
\]

where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.

For a square pyramid, the base is a square, so the area of the base \( B \) can be expressed as \( s^2 \) (where \( s \) is the length of one side of the base). Thus, we can rewrite the formula for the volume as:

\[
V = \frac{1}{3} \times s^2 \times h
\]

Given that the volume \( V \) is 2400 cubic centimeters and the height \( h \) is 18 centimeters, we substitute these values into the formula:

\[
2400 = \frac{1}{3} \times s^2 \times 18
\]

Next, we simplify the equation:

\[
2400 = 6s^2
\]

Dividing both sides by 6:

\[
s^2 = \frac{2400}{6}
\]

\[
s^2 = 400
\]

Taking the square root of both sides, we find:

\[
s = \sqrt{400} = 20 \text{ centimeters}
\]

Thus, the approximate base length of the pyramid is:

**C. 20.0 centimeters**