Question

The radius of he base and the height of a cylinder are in the ratio 2:3.If its volume is 1617 $c{m}^2$ ,find the total surface area of the cylinder.

Answer 1

Solution:-
r : h = 2 : 3
r/h = 2/3
3r = 2h
h = 3r/2
Now, $\pi r^{2}h$ = 1617 cu cm
22/7 x $r^2$ x 3r/2 = 1617
$r^3=(1617\times 7\times 2)÷(22\times 3)$
$r^3$ = 343
r = $3\sqrt{3}43$
r = 7 cm
Then the height = 10.5 cm
Surface area of the cylinder = $2\pi r(r+h)$
= $(2\times 22/7\times 7)\times (7+10.5)$
= $44\times 17.5$
= 770 sq cm
Answer