Question

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 1

Given :-

• Ratio of radius and height = 2 : 3

• CSA of cylinder = 300 π cm²

• Value of π = 3.14

To Find :-

• Volume of the cylinder

Solution :-

Let's :-

Radius of cylinder = 2x

Height of cylinder = 3x

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

Radius = 2x = 2 × 5 = 10 cm

Height = 3x = 3 × 5 = 15 cm

Now

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

★ Volume of cylinder is 4710 cm³

Answer 2

Step-by-step explanation:

Given:-

• The radius and the height of a cylinder are in the ratio 2 : 3

• Curved surface area of the cylinder = 300πcm².

To Find:-

• The Volume of the cylinder.

Solution:-

Let the common ratio between radius and e

height be x

The radius of cylinder = 2x

The height of cylinder = 3x

Given, CSA of cylinder = 300π cm²

As we know that

The curved surface area(CSA) of the cylinder is given by the formula:-

$\boxed{ \rm \leadsto CSA \: of \: cylinder \: = 2\pi rh}$

Here:-

• r = radius

• h = height

Substituting the values:-

$\rm \implies 300\pi \: = 2\pi rh$

$\rm \implies 300\pi \: = 2\pi (2x)(3x)$

$\rm \implies 300 \: = 2(2x)(3x)$

$\rm \implies 300 \: =12 {x}^{2}$

$\rm \implies \dfrac{ 300}{12} \: ={x}^{2}$

$\rm \implies 25 \: ={x}^{2}$

$\rm \implies \sqrt{25} \: ={x}$

$\rm \implies 5 \: ={x}$

$\rm \implies x = 5$

The radius of the cylinder = 2x = 2 × 5 = 10cm

The radius of the cylinder = 2x = 2 × 5 = 10cmThe height of the cylinder = 3x = 3 × 5 = 15cm

Now;

$\boxed{\leadsto \rm Volume \: of \: cylinder =\pi {r}^{2} h}$

Substituting the values:-

$\rm \implies \pi {r}^{2} h$

$\rm \implies 3.14 \times {10}^{2} \times 15$

$\rm \implies 3.14\times {100}\times 15$

$\rm \implies 314\times 15$

$\rm \implies 4710$

Therefore:-

Volume of cylinder = 4710cm³