Question

A solid toy is the form of a right circular cylinder with a hemispherical shape at the one end and a cone at the other end. Their diameter is $4.2cm$ and the heights of the cylindrical and conical portions are $12cm$ and $7cm$ respectively. Find the volume of the toy.

• A. 210.172 cm${}^3$
• B. 217.864 cm${}^3$
• C. 220.232 cm${}^3$
• D. 252.64 cm${}^3$

Answer 1

The correct option is B 217.864 cm${}^3$

$r=2.1$ $cm$

$h_1=12$ $cm$

$h_2=7$ $cm$

Volume of cylinder $=\pi r^2{h}_1=\pi \cdot (2.1{)}^2\cdot (12)=166.25$ $c{m}^3$

Volume of hemisphere $=\frac{2}{3}\pi r^3=\frac{2}{3}\pi (2.1{)}^3=19.396$ $c{m}^3$

Volume of cone $=\frac{1}{3}\pi r^2{h}_2=\frac{1}{3}\pi \left(2.1{)}^2\right(7)=32.32$ $c{m}^3$

Total Volume $=$ Add these $3$ volumes $=217.966$ $c{m}^3$