Question

1. what is the volume of the bottom prism in cm³?

part c: guided practice

1. what is the radius of a circle?
2. if the diameter of the circle to the right is 4 cm, what would be its radius in cm?

Explanation:

For the volume of the rectangular prism (bottom prism):

Step1: Recall the formula for the volume of a rectangular prism

The volume \( V \) of a rectangular prism is given by the formula \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Identify the values of length, width, and height

From the diagram, the length \( l = 6 \, \text{cm} \), the width \( w = 4 \, \text{cm} \), and the height \( h = 5 \, \text{cm} \).

Step3: Substitute the values into the formula

\( V = 6 \times 4 \times 5 \)

Step4: Calculate the product

First, multiply \( 6 \times 4 = 24 \). Then, multiply \( 24 \times 5 = 120 \).

The radius of a circle is the distance from the center of the circle to any point on its circumference. It is also half of the diameter of the circle, i.e., if \( d \) is the diameter, then the radius \( r=\frac{d}{2} \).

Step1: Recall the relationship between diameter and radius

The formula relating the diameter \( d \) and radius \( r \) of a circle is \( r=\frac{d}{2} \).

Step2: Substitute the given diameter value

Given that the diameter \( d = 4 \, \text{cm} \), substitute into the formula: \( r=\frac{4}{2} \).

Step3: Calculate the radius

\( \frac{4}{2}=2 \).

Answer:

The volume of the bottom prism is \( 120 \, \text{cm}^3 \).

For Part C, Question 1: