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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.

 Jul 15, 2021
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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.

laugh  !

 Jul 15, 2021

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