Question

A pencil grip is shaped like a triangular prism with a cylinder removed from the middle. The base of the prism is a right isosceles triangle with leg lengths of 2 centimeters. The diameter of the base of the removed cylinder

is 1 centimeter. The heights of the prism and the cylinder are the same and equal to 4 centimeters. What is
the exact volume of the pencil grip?

Answer 1

Answer: 4.858 cm^3

Explanation:

The prism's base is a right isosceles triangle with leg lengths' of b = 2

The diameter of the base of the removed cylinder is d = 1

The heights of the prism and the cylinder are the same, and equal to h = 4

`V &= V_(p) - V_(c) \\ &= b h - \left( \pi \ r^2 \ h \right) \\ &= 2 * 4 - \left( \pi * \left( (1)/(2) \right)^2 * 4 \right) \\ &= 8 - \left( 4 \pi * \left( 0.5\right)^2 \right) \\ &= 8 - \left( 4 \pi * 0.25 \right) \\ &= 8 - \pi \\ \therefore V &= 4.858`

Therefore, the volume of the pencil grip is approximately 4.858 cm^3