Question

a glass sculpture is shaped like a triangular pyramid. the volume of the sculpture is 120 cubic centimeters, and its height (from the apex to the center of the triangular base) is 10 centimeters.
what is the area of the triangular base of the sculpture? round your answer to the nearest tenth.
use the keypad to type your answer in the box provided.
the area of the triangular base of the sculpture is square centimeters.

Explanation:

Step1: Recall the volume formula for a triangular pyramid

The volume formula for a triangular pyramid is \(V=\frac{1}{3}Bh\), where \(V\) is the volume, \(B\) is the area of the base, and \(h\) is the height.

Step2: Rearrange the formula to solve for \(B\)

We can rewrite the formula \(V = \frac{1}{3}Bh\) as \(B=\frac{3V}{h}\).

Step3: Substitute the given values into the formula

Given \(V = 120\) cubic centimeters and \(h=10\) centimeters. Then \(B=\frac{3\times120}{10}\).
First, calculate \(3\times120 = 360\). Then \(\frac{360}{10}=36\).

Answer:

36