# 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
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?

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.

### Relevant Questions

When a gas is taken from a to c along the curved path in the figure (Figure 1) , the work done by the gas is W = -40 J and the heat added to the gas is Q = -140 J . Along path abc, the work done by the gas is W = -50 J . (That is, 50 J of work is done on the gas.)
I keep on missing Part D. The answer for part D is not -150,150,-155,108,105( was close but it said not quite check calculations)
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Part D
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Express your answer to two significant figures and include the appropriate units.
Part E
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