Question

A cylinder has a diameter of 20 cm. The area of the curved surface is $100c{m}^2$(sq.cm).

Find:

(i) the height of the cylinder correct to one decimal place.

(ii) the volume of the cylinder correct to one decimal place.

Answer 1

diameter = 20 cm
radius = $\frac{20}{2}$ = 10 cm
curved surface area = 100 $c{m}^2$
we know,
$\frac{22}{7}\times r\times l$ = curved surface area
therefore, $\frac{22}{7}\times 10\times l$ =100
l = $\frac{100}{10}\times \frac{7}{22}$
l =$\frac{35}{11}$
= 3.78
we know,
$slantheigh{t}^2=heigh{t}^2+radiu{s}^2$
height = 9.2 cm
volume = $\frac{22}{7}\times r^2\times h$
= $\frac{22}{7}\times 10\times 10\times 9.2$
=2891.4 $c{m}^3$
height = 9.2 and volume = 2891.4 $c{m}^3$