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A solid metal prism has a rectangular base with sides of 4 i...
JMAP math geometry
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A solid metal prism has a rectangular base with sides of 4 inches and 6 inches, and a height of 4 inches. A hole in the shape of a cylinder, with a radius of 1 inch, is drilled through the entire length of the rectangular prism.

What is the approximate volume of the remaining solid, in cubic inches?

1) 19

2) 77

3) 93

4) 96

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judziy
Asked by judziyrep:2.0K
University of Benin Nigeria
24 June 2020

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peter
Peter answeredrep:1.8K
University of Lagos Nigeria
12 August 2020
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Since a cylindrical hole is drilled into the prism, the remaining volume, V will be the entire volume of the prism, V1 minus the volume of the drilled cylindrical shape, V2. That is,

V = V1 + V2

Where V1 and V2 are the volumes of the prism and cylinder respectively.

V1 = Length x Width x Height

V1 = 4 x 6 x 4

V1 = 96

V= πr2h

Where r is the radius and h is the height

V= π(1)2(6)

V= 19

Thus, V = 96 - 19

= 77

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