Q32. - Geometry

Question

A right prism has square bases with edges that are three times as long as the lateral edges. The prism’s total area is 750 m². Find the volume.

Step-by-Step Solution

Answer

The volume of prism is$288m^3$ .

Step 1. Given information.

A right prism has square bases with edges that are three times as long as the lateral edges and the total area is${\text{750m}}^2$ .

Step 2. Consider the variable.

Let the lateral edges is x.

Then, the edges of square are 3x.

Step 3. Determine the total volume.

To find the area, multiply the base area and height,

$\begin{array}{c}v=bh\\ =\frac{5+11}{2}\left(4\right)\left(9\right)\text{ [substitute]}\\ =288m^3\text{ [simplify]}\end{array}$

Thus, the volume of prism is$288{\text{\hspace{0.17em}m}}^3$ .