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?
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
V2 = πr2h
Where r is the radius and h is the height
V2 = π(1)2(6)
V2 = 19
Thus, V = 96 - 19