Question

- The radii of two cylinders are in the ratios 2:3 and their heights are in the ratio 3:5. the ratio of their curved surface area is
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Answer 1

Answer:

• The area of their curved surface area is 2 : 5.

Given:

• The radii of two cylinders are in the ratios 2:3 and their heights are in the ratio 3:5.

To find:

• The ratio of their curved surface area.

Solution:

Let the constant for the radius be R and for the height be H.

$\boxed{\sf{Curved \ surface \ area \ of \ cylinder=2\pi rh}}$

$\sf{\therefore{Ratio \ for \ curved \ surface \ area \ can \ be}} \\ \\ \\ \sf{Ratio=\dfrac{2\times\pi\times2R\times3H}{2\times\pi\times3R\times5H}} \\ \\ \\ \sf{\therefore{Ratio=\dfrac{2R\times3H}{3R\times5H}}} \\ \\ \\ \sf{\therefore{Ratio=\dfrac{2\times3}{3\times5}}} \\ \\ \\ \sf{\therefore{Ratio=\dfrac{2}{5}}} \\ \\ \\ \sf{\therefore{Ratio=2:5}}$

Therefore, the ratio of their curved surface area is 2 : 5.