Question

The radius and height of a cylinder are in the ratio of 7:2. lf the volume of the cylinder is 8316cm³,find the radius and height of the cylinder​

Answer 1

Given :-

The radius and height of a cylinder are in the ratio of 7:2. lf the volume of the cylinder is 8316cm³

To Find :-

Radius and height

Solution :-

Le the radius be 7x and height be 2x

Volume = πr²h

8316 = 22/7 × (7x)² × 2x

8316 = 22/7 × 49x² × 2x

8316 × 7/22 = 98x³

378 × 7 = 98x³

378 × 7/98 = x³

378 × 1/14 = x³

27 = x³

∛27 = x

3 = x

Therefore

Radius = 7x = 7(3) = 21 cm

Height = 2x = 2(3) = 6 cm

Answer 2

Answer:

$\green{ \boxed{ \odot \sf \: radius \: \: r = 21 \: cm}} \\ \\ \green{ \boxed{ \odot \sf \: height \: \: h = 6\: cm}}$

Explanation :

Given,

★ Radius and Height of the Cylinder are in ratio

= 7 : 2

★ Volume of Cylinder is = 8316 cm³.

To find :

$\sf \: \odot \: radius \: of \: the \: cylinder \: \: = r \\ \sf \odot \: height \: of \: the \: cylinder \: \: = \: h$

Solution :

Let x be the common in given ratios.

So,

Radius = 7x

Height = 2x

We know that,

$</strong><strong>\</strong><strong>p</strong><strong>i</strong><strong>n</strong><strong>k</strong><strong>{</strong><strong>\sf \: Volume \: of \: a \: cylinder = \pi {r}^{2} </strong><strong>h</strong><strong>}</strong><strong>$

According to the question,

$\sf \: \: \: \: \: \: \: \pi {r}^{2} h = 8316 \\ \sf \implies \: 3.14 \times {(7x)}^{2} \times 2x = 8316 \\ \sf \implies \: 3.14 \times 49 {x}^{2} \times 2x \\ \sf \implies \: {x}^{3} = \frac{8316}{3.14 \times 49 \times 2} \\ \sf \implies \: {x}^{3} = 27.024 \\ \sf \implies \: x = \sqrt[3]{27.024} \\ \sf \implies \: x = 3 \: \: cm \\ \\ \: \bf \: radius \: \: r = 7x = 7 \times 3 = 21 \: cm \\ \bf \: height \: \: h = 2x = 2 \times 3 = 6 \: cm$