Question

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is $12cm$ and it's base radius is $4.2cm,$ find the total surface area of the article. Also, find the volume of the wood left in the article.

Answer 1

Height of the cylinder $=12cm$

Radius of base $=4.2cm$

The total surface area of the object

$=$ Curved surface area of the cylinder $+2\times$Curved surface area of the hemispherical surface

$=2\pi rh+2\times 2\pi r^2$

$=2\pi r(h+2r)$

$=2\times \frac{22}{7}\times 4.2(12+2\times 4.2)$

$=44\times 0.6\times 20.4c{m}^2$

$=538.56c{m}^2$
The volume of wood left in the article
=Volume of cylinder - Volume of 2 hemispheres

$=\pi r^{2}h-2\times \frac{2}{3}\pi r^3$

$=\pi r^2(h-\frac{4}{3}r)$

$=\frac{22}{7}\times 4.2\times 4.2(12-\frac{4}{3}\times 4.2)c{m}^3$

$=22\times \frac{6}{10}\times \frac{42}{10}\times \frac{64}{10}$

$=354.816c{m}^3$