CPM Homework Help : GC Problem 10-6

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10-6.

A rectangular prism has a cylindrical hole removed, as shown at right. If the radius of the cylindrical hole is $2$ inches, find the volume and total surface area of the solid.

Hint (volume):

Step 1 (volume):

Find the volume of the cube.

Step 2 (volume):

Find the volume of the cylinder within the cube.

Step 3 (volume):

Subtract the volume of the cylinder from the volume of the cube.

Answer (volume):

$139.5 \; \text{in}^3$

Hint (surface area):

Step 1 (surface area):

Find the surface area of the cube.

Step 2 (surface area):

Find the surface area of the cylinder.

Step 3 (surface area):

Add the surface area of the cube and the lateral area of the cylinder, but subtract the area of the two holes (circles).

Answer (surface area):

$311.4 \; \text{in}^2$