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A company is creating an object from a wooden cube with an edge length of 8.5 cm. A right circular cone with a diameter of 8 cm and an altitude of 8 cm will be cut out of the cube. Which expression represents the volume of the remaining wood?
JMAP geometry math cone prism
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A company is creating an object from a wooden cube with an edge length of 8.5 cm. A right circular cone with a diameter of 8 cm and an altitude of 8 cm will be cut out of the cube. Which expression represents the volume of the remaining wood?

1) (8.5)3 − π(8)2 (8)

2) (8.5)3 − π(4)2 (8)

3) (8.5)3 − 1/3 π(8)2 (8)

4) (8.5)3 − 1/3 π(4)2 (8)

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judziy
Asked by judziyrep:909
University of Benin Nigeria
24 June 2020

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peter
Peter answeredrep:938
University of Lagos Nigeria
12 August 2020
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Since a cone will be cut out of the cube, the remaining volume will be the volume of the entire cube minus volume of the cone. That is,

V = V1 - V2

where V1 and V2 are the volume of the cube and cone respectively.

V1 = S2

Where S is the length of each sides of the cube.

V= 8.53

V2 =1/3  πr2h

Where r is the radius and h is the height

radius = daimeter/2

radius = 8/2 = 4

V2 = 1/3 π(4)2(8)

Thus, V = (8.5)3 - 1/3 π(4)2(8)

Ans 4

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