Question

With reference to the figure given above a metal container in the form of a cylinder is surmounted by hemisphere of the same radius. The internal height of the cylinder is $7m$ and the internal radius is $3.5m$
(i) the total area of the internal surface excluding the base:
(ii) The internal volume of the container in $m^3$.
(Take $\pi$ to be $\frac{22}{7}$.)

Answer 1

(i) Total internal surface area

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

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

$=154+77$

$=231sq.meter$

(ii) Internal volume of the container

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

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

$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}(7+\frac{2}{3}\times \frac{7}{2})$

$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\frac{28}{3}$

$=125\times \frac{7}{3}=\frac{1078}{3}=359.33m^3$

Internal volume $=359.33m^3$