Question

question 17 of 20 :
select the best answer for the question.

1. in the figures below, the cube - shaped box is 6 inches wide and the rectangular box is 10 inches long, 4 inches wide, and 4 inches high. how much greater is the volume of the cube - shaped box than the rectangular box?

a. 60 cubic inches
b. 50 cubic inches
c. 56 cubic inches
d. 66 cubic inches

Explanation:

Step1: Calculate volume of cube

A cube has side length \( s = 6 \) inches. The volume of a cube is \( V_{cube}=s^3 \). So, \( V_{cube}=6^3 = 6\times6\times6 = 216 \) cubic inches.

Step2: Calculate volume of rectangular box

A rectangular box (prism) has length \( l = 10 \) inches, width \( w = 4 \) inches, height \( h = 4 \) inches. The volume of a rectangular prism is \( V_{rect}=l\times w\times h \). So, \( V_{rect}=10\times4\times4 = 160 \) cubic inches.

Step3: Find the difference

Subtract the volume of the rectangular box from the volume of the cube: \( 216 - 160 = 56 \) cubic inches.

Answer:

C. 56 cubic inches