Answer: 4.858 cm^3
Step-by-step 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
[tex]V &= V_{p} - V_{c} \\ &= b h - \left( \pi \ r^2 \ h \right) \\ &= 2 \times 4 - \left( \pi \times \left( \frac{1}{2} \right)^2 \times 4 \right) \\ &= 8 - \left( 4 \pi \times \left( 0.5\right)^2 \right) \\ &= 8 - \left( 4 \pi \times 0.25 \right) \\ &= 8 - \pi \\ \therefore V &= 4.858[/tex]
Therefore, the volume of the pencil grip is approximately 4.858 cm^3
