Question

A right circular cylinder and right circular cone have equal bases abd equal heights . If their CSA are in ration 8:5, determine the ratio of base to the height of either of them.

Answer 1

↑ Here is your answer ↓
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Let radius be 'r' and height be 'h'.

$\frac {2 \pi r h} { \pi rl} = \frac 8 5$

$5h = 4l$

$5h = 4 \sqrt{h^2 + r^2}$ [∵ $l = \sqrt{h^2 + r^2}$]

$25h^2 = 16[h^2 + r^2]$ (Squaring both sides)

$25h^2 = 16r^2 + 16h^2$

$9h^2 = 16 r^2$

$\frac{r^2}{h^2} = \frac{9}{16}$

So, r:h = 3:4

Answer 2

Hope this may help you