Question

a prism has a volume of 900 cubic meters. if a pyramid has the same base area and height, what is the volume of the pyramid? use the keypad to type your answer in the box provided. the volume of the pyramid is cubic meters.

Explanation:

Step1: Recall the volume formulas

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

Step2: Relate the volumes

Since the pyramid and the prism have the same base area \(B\) and height \(h\), and \(V_{prism}=900 = B\times h\). Then \(V_{pyramid}=\frac{1}{3}\times V_{prism}\).

Step3: Calculate the volume of the pyramid

Substitute \(V_{prism} = 900\) into the formula for \(V_{pyramid}\). So \(V_{pyramid}=\frac{1}{3}\times900\).

$$V_{pyramid}=300$$

Answer:

300