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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

**Comments**

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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, V_{1} minus the volume of the drilled cylindrical shape, V_{2}. That is,

V = V_{1} + V_{2}

Where V_{1} and V_{2} are the volumes of the prism and cylinder respectively.

V_{1} = Length x Width x Height

V_{1} = 4 x 6 x 4

V_{1} = 96

V_{2 }= πr^{2}h

Where r is the radius and h is the height

V_{2 }= π(1)^{2}(6)

V_{2 }= 19

Thus, V = 96 - 19

= 77

**Ans 2**

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