Question

The radii of two right circular are in the ratio 2:3 and their heights are in the ratio 5:4 . calculate the ratio of their curved surface areas . ​

Answer 1

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☯ ƛɳʂɯҽɾ ☯

⇨Let radii of the cylinders be r1 = 2r, r2 = 3r.

⇨Height of the cylinders be h1 = 5h , h2 = 4h.

⇨ The curved surface areas are

$\small \: Surface \: 1 = 2\pi \: r1 \: h1 \\ = 2\pi.2r.5h \\ = 20\pi \: r \: h$

$\small \: Surface \: 2 \: = 2\pi \: r2 \: h2 \\ = 2\pi.3r.4h \\ = 24\pi \: rh$

$\small \: S1:S2 = 20\pi \: rh:24\pi \: rh \\ = 20:24 = 5:6$

Hence , the ratio of curved surface areas is 5:6 .

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