Question

With reference to the given figure. a metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and internal radius is 3.5 m. Calculate: [4 MARKS]
(i) The total area of the internal surface excluding the base
(ii) The internal volume of the container in $m^3$.
$(Use\pi =\frac{22}{7})$

Answer 1

Each Part: 2 Marks

(i) Total area of the internal surface excluding the base
= Curved surface area of hemisphere + Curved surface area of cylinder
$=2\pi r^2+2\pi rh=2\pi r(r+h)=2\times \frac{22}{7}\times 3.5\times (3.5+7)=\frac{44}{7}\times 3.5\times 10.5=44\times 0.5\times 10.5=22\times 10.5=231m^2$
(ii) Internal volume of the container = Volume of hemisphere + Volume of cylinder
$=\frac{2}{3}\pi r^3+\pi r^{2}h=\pi r^2(\frac{2}{3}r+h)=\frac{22}{7}\times 3.5\times 3.5\times (\frac{2}{3}\times 3.5+7)=11\times 3.5\times (\frac{7}{3}+7)=11\times 3.5\times \frac{28}{3}=359.33m^3$