A carpenter chisels a square hole of side 2 in. through a round post of radius 2 in. The axis of the hole

intersecting that of the post at right angles. Find the volume of the wood cut out.

Guest Jul 15, 2021

#1**+2 **

A carpenter chisels a square hole of side 2 in. through a round post of radius 2 in. The axis of the hole

intersecting that of the post at right angles. Find the volume of the wood cut out.

**Hello Guest!**

The face of the side of the body is made up of two segments of a circle and four right triangles.

\(A_{ segment}=\frac{\pi r^2}{6}=\frac{\pi \cdot2^2in^2}{6}=\color{blue}\frac{2}{3}\pi\ in^2\)

\(A_{triangle }=\frac{2\cdot sin(30°)\cdot 1 }{2}=\color{blue}\frac{1}{2}in^2\)

\(A_{body}=2\cdot A_{ segment}+4\cdot A_{triangle }=2\cdot \frac{2}{3}\pi\ in^2+4\cdot \frac{1}{2}in^2=\color{blue}6.189\ in^2\)

\(V_{body}=A_{body}\cdot 2\ in\\ V_{body}=6.189\ in^2\cdot 2\ in\\ \color{blue}V _{body}=12.378\ in^3\)

The carpenter cut 12.378 cubic inches of wood from the log.

!

asinus Jul 15, 2021