Question

cassandra wants to package an inflated soccer ball in a cardboard box. the diameter of the soccer ball is 22 cm. what is the volume of the smallest rectangular prism - shaped box that can enclose the soccer ball?
a. 484 cm³
b. 1,331 cm³
c. 10,648 cm³
d. 85,184 cm³

Explanation:

Step1: Determine box dimensions

The soccer ball (a sphere) has a diameter of 22 cm. For the smallest rectangular prism (box) to enclose it, the box must be a cube (or rectangular prism with length, width, height equal to the ball's diameter) since the ball's diameter is the maximum distance across. So length \( l = 22 \, \text{cm} \), width \( w = 22 \, \text{cm} \), height \( h = 22 \, \text{cm} \).

Step2: Calculate volume of rectangular prism

The formula for the volume \( V \) of a rectangular prism is \( V = l \times w \times h \). Substituting the values:
\[
V = 22 \times 22 \times 22
\]
First, calculate \( 22 \times 22 = 484 \), then \( 484 \times 22 = 10648 \, \text{cm}^3 \).

Answer:

C. \( 10648 \, \text{cm}^3 \)