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प्रश्न
A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8 : 5, determine the ratio of the radius of the base to the height of either of them.
उत्तर
For right circular cylinder, let r1 = r, h1 = h.
Then, curved surface area, s1 of cylinder = `2pir_1 = 2pirh ........... (1)`
For right circular cone, let r2 = r, h2 = h
Then, curved surface area, s2 of cone = `pi r_2l " where "l = sqrt(r_2^2 + h_2^2) = sqrt(r^2 + h^2)`
` = pir sqrt(r^2 + h^2) ..................(2)`
Divide (i) and (ii),
`s_1/s_2 = (2pirh)/(pirsqrt(r^2 + h^2))`
`8/5 = (2h)/sqrt(r^2 + h^2) [s_1/s_2 = 8/5]`
`64/25 = (4h^2)/(r^2 + h^2)` [squaring]
`64r^2 + 64h^2 = 100h^2`
`64r^2 = 36h^2`
`16r^2 = 9h^2`
`r^2 / h^2 = 9/16`
`r/h = 3/4`
`therefore r : h = 3:4`
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