Question

the volume of a prism is 420 cubic units. what is the volume of a pyramid that shares the same base area and height as this prism? use the keypad to type your answer in the box provided. the volume of the pyramid is cubic units.

Explanation:

Step1: Recall the volume formulas

The volume formula of a prism is \(V_{prism}=B\times h\) (where \(B\) is the base area and \(h\) is the height). The volume formula of a pyramid is \(V_{pyramid}=\frac{1}{3}\times B\times h\).

Step2: Use the relationship between the two volumes

Since the pyramid and the prism have the same base area \(B\) and height \(h\), and \(V_{prism}=B\times h = 420\) cubic units. Then \(V_{pyramid}=\frac{1}{3}\times V_{prism}\).

Step3: Calculate the volume of the pyramid

Substitute \(V_{prism} = 420\) into the formula for \(V_{pyramid}\): \(V_{pyramid}=\frac{1}{3}\times420\).

$$ \frac{1}{3}\times420=\frac{420}{3}=140 $$

Answer:

140