Question

thr radius and height of a cylinder are in the ratio 7:2 if the TSA of a cylinder is 2772cm^2 find the radius and height of a cylinder​

Answer 1

Step-by-step explanation:

Given:-

• The radius and height of a cylinder are in the ratio 7 : 2.

• The Total surface area of the cylinder (TSA) = 2772cm²

To Find:-

• The radius of the cylinder.

• The height of the cylinder.

Solution:-

Let the common ratio between the radius and height be x

So:-

The radius of the cylinder (r) = 7x

And height of the cylinder (h) = 2x

Given, TSA of the cylinder = 2772cm²

$\boxed{ \sf TSA \: of \: a \: cylinder = 2\pi r(h + r)}$

$\sf \implies 2\pi r(h + r) = 2772$

$\sf \implies 2\pi \times (7x) \big[2x+ 7x\big] = 2772$

$\sf \implies 2\pi \times 7x \times 9x = 2772$

$\sf \implies 2 \times \dfrac{22}{7} \times 7x \times 9x = 2772$

$\sf \implies 2 \times 22 \times (x) \times 9x = 2772$

$\sf \implies 396x^2 = 2772$

$\sf \implies x^2 = \dfrac{2772}{396}$

$\sf \implies x^2 = 7$

$\sf \implies x = \sqrt{7}$

$\sf The\: radius = 7x = 7 \times \sqrt{7} = 7\sqrt{7}$

$\sf The\: height = 2x = 2\times \sqrt{7} = 2\sqrt{7}$

$\underline{\boxed{\sf The \: radius \: of \: the \: cylinder = 7\sqrt{7}cm}}$

$\underline{\boxed{\sf The \: height \: of \: the \: cylinder = 2\sqrt{7}cm}}$

Answer 2

Question:

The radius and height of a cylinder are in the ratio 7:2 if the TSA of a cylinder is 2772cm² find the radius and height of a cylinder.

Given: The radius and height of cylinder are in ratio 7:2.

Total surface area of cylinder = 2772 cm².

To find: Radius and height of cylinder.

Solution: Radius and height of cylinder are in ratio 7:2.

Let the radius of cylinder = 7x

Let the height = 2x

TSA of cylinder = 2772cm²

Formula : 2πr(r+h)

=> 2πr(r+h) = 2772

=> 2π (7x) [7x+2x]=2772

=> 2π (7x) (9x)=2772

=> 2 × (22/7) × (7x) × (9x) = 2772

=> 2 × (22) × (9x)² = 2772

=> 396 x² = 2772

=> x² = 2772/396

=> x²= 7

=> x =√7

Therefore,

The radius of cylinder = 7x =7(√7)

The height of cylinder = 2x = 2(√7)