A machine part is made from a rectangular prism with a smaller rectangular prism cut out of it, as shown below. What is the volume of the part? Circle the correct answer. A 20 cubic centimeters B 140 cubic centimeters C 160 cubic centimeters D 180 cubic centimeters Leo chose D as the correct answer. How did he get that answer?

A machine part is made from a rectangular prism with a smaller rectangular prism cut out of it, as shown below. What is the volume of the part? Circle the correct answer. A 20 cubic centimeters B 140 cubic centimeters C 160 cubic centimeters D 180 cubic centimeters Leo chose D as the correct answer. How did he get that answer?

Question
Solid Geometry
asked 2021-01-07
A machine part is made from a rectangular prism with a smaller rectangular prism cut out of it, as shown below. What is the volume of the part? Circle the correct answer.
A 20 cubic centimeters
B 140 cubic centimeters
C 160 cubic centimeters
D 180 cubic centimeters
Leo chose D as the correct answer. How did he get that answer?

Answers (1)

2021-01-08
The volume of the part is the difference of the volume of the larger rectangular prism and the smaller rectangular prism so we have:
Vpart=Vlarger−Vsmaller
The volume of a retangular prism is V=lwh. For the larger prism, l=8 cm, w=4 cm, and h=5 cm. For the smaller prism, l=4 cm, w=1 cm, and h=5 cm. So,
Vpart=(8)(4)(5)−(4)(1)(5)
Vpart=160−20
Vpart=140 cm^3
So, the correct answer is choice B.
Leo chose D because instead of subtracting, he added the volume of the prisms which is incorrect.
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