1.

the radius and the height of a cylinder are in the ratio 2:3 if it's curved surface area is 300π cm² find its volume(take π=3.14)​

Answer»

GIVEN :-

  • Ratio of radius and height = 2 : 3

  • CSA of cylinder = 300 π cm²

  • Value of π = 3.14

To Find :-

Solution :-

Let's :-

Radius of cylinder = 2x

Height of cylinder = 3x

\large \implies \boxed{ \sf CSA \: of \: cylinder = 2\pi rh} \\ \\ \implies \tt2 \times \pi \times 2x \times 3x = 300\pi \\ \\ \implies \tt12x^2 = 300 \\ \\ \implies \tt x^2 = \frac{300}{12} \\ \\ \implies \tt x = \sqrt{25} \\ \\ \implies \tt x =<klux>5</klux>

Radius = 2x = 2 × 5 = 10 cm

Height = 3x = 3 × 5 = 15 cm

Now

\large \implies\boxed{\sf Volume \: of \: cylinder = {\pi r}^{2} h }\\ \\\implies \tt 3.14 \times {<klux>10</klux>}^{2} \times 15 \\ \\\implies \tt 3.14 \times 100 \times 15 \\ \\\implies \tt 314 \times 15 \\ \\\implies \tt 4710 \: {cm}^{3}

★ Volume of cylinder is 4710 cm³


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