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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)

**Comments**

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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 = V_{1} - V_{2}

where V_{1} and V_{2} are the volume of the cube and cone respectively.

V_{1} = S^{2}

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

V_{1 }= 8.5^{3}

V_{2} =1/3 πr^{2}h

Where r is the radius and h is the height

radius = daimeter/2

radius = 8/2 = 4

V_{2} = 1/3 π(4)^{2}(8)

Thus, V = (8.5)^{3} - 1/3 π(4)^{2}(8)

**Ans 4**

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