Question

liam uses a machine to polish specific pieces of metal. this machine is shaped like a rectangular prism. it measures 30 inches long, 12 inches wide, and 20 inches high. he fills the machine up to the mark that is 6 inches below the top with cleaner. how many cubic inches of cleaner does liam put in the machine? a) 3,600 cubic inches b) 5,040 cubic inches c) 5,760 cubic inches d) 7,200 cubic inches

Explanation:

Step1: Find the height of the cleaner

The machine's total height is 20 inches, and the cleaner is filled 6 inches below the top. So the height of the cleaner is $20 - 6 = 14$ inches.

Step2: Calculate the volume of the cleaner

The volume \( V \) of a rectangular prism is given by the formula \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. Here, \( l = 30 \) inches, \( w = 12 \) inches, and \( h = 14 \) inches. So \( V = 30 \times 12 \times 14 \). First, calculate \( 30 \times 12 = 360 \). Then, \( 360 \times 14 = 5040 \) cubic inches.

Answer:

B) 5,040 cubic inches