Question

using the given information, draw and label a diagram of each of the following 3 - d figures. then find the volume of each solid.

1. a right prism with a square base, 4 inches on a side, and a height of 10 inches.
2. a right cylinder with a circular base of radius 2 inches and a height of 10 inches.

Explanation:

Problem 1: Right Prism with Square Base

Step1: Recall Volume Formula for Prism

The volume \( V \) of a prism is given by \( V = B \times h \), where \( B \) is the area of the base and \( h \) is the height of the prism.

Step2: Calculate Base Area (Square)

The base is a square with side length \( s = 4 \) inches. The area of a square is \( B = s^2 \). So, \( B = 4^2 = 16 \) square inches.

Step3: Calculate Volume

Substitute \( B = 16 \) and \( h = 10 \) into the volume formula: \( V = 16 \times 10 = 160 \) cubic inches.

Step1: Recall Volume Formula for Cylinder

The volume \( V \) of a cylinder is given by \( V = \pi r^2 h \), where \( r \) is the radius of the base and \( h \) is the height of the cylinder.

Step2: Substitute Values

Given \( r = 2 \) inches and \( h = 10 \) inches. Substitute into the formula: \( V = \pi \times (2)^2 \times 10 \).

Step3: Simplify

First, calculate \( (2)^2 = 4 \). Then, \( V = \pi \times 4 \times 10 = 40\pi \) (or approximately \( 125.66 \)) cubic inches.

Answer:

The volume of the right prism is \( \boldsymbol{160} \) cubic inches.

Problem 2: Right Cylinder