Question

A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10 units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units.
Which expression represents the volume, in cubic units, of the shaded region of the composite figure?

One-half(14)(10)(8) – π(2.52)(8)
One-half(14)(10)(8) + π(2.52)(8)
One-third (one-half)(10)(8)(14) – π(2.52)(8)
One-third (one-half)(10)(8)(14) + π(2.52)(8)

Answer 1

The volume is prism volume minus cylinder volume. Prism: area = 1/2·14·10, so V = (1/2·14·10)·8. Cylinder: V = π(2.5^2)·8.

Thus the correct expression is:
One-half(14)(10)(8) – π(2.52)(8).