Question

8. The volume of a cylinder is 5346 cm3. and the ratio of its radius to its height is 3: 7. Find
its radius and height.​

Answer 1

The radius of a cylinder(r) = 9 cm and The height of a cylinder(h) = 21 cm

The volume of a cylinder = 5346

Let 3x and 7x be the radius and height of a cylinder.

To find, the radius(r) and height(h) of the cylinder = ?

We know that,

The volume of a cylinder = πr^2h

⇒ 22/7 × (3x)^2×7x = 5346

⇒ 22×9x^2 = 5346

⇒ 198x^2 = 5346

⇒ x^3 = 5346/198 = 27

⇒ x^3 = 3^3

⇒ x = 3 cm

∴ The radius of a cylinder(r) = 3 × 3 cm = 9 cm and

The height of a cylinder(h) = 7 × 3 cm = 21 cm

Step-by-step explanation:

hope it helps u...

Answer 2

$\bigstar$$\mid$ GIVEN :-

• The ratio of the cylinder's height and radius is 3:7.
• The area of the cylinder is $\bf 5346cm^3$.

$\bigstar$$\mid$ TO FIND :-

• The radius and the height of the cylinder.

$\bigstar$$\mid$ SOLUTION :-

• Let's assume that the radius height and the is 3x and 7x respectively.

Using the formula :

$\sf \green \dag{ \underline{ \boxed{\bf \pi r^2h}}} \green \dag$

$\to \sf \frac{22}{7} \times {(3x)}^{2} \times 7x = 5346 {cm}^{3} \\ \sf \to \: \frac{22}{ \cancel7} \times 9 {x}^{2} \times \cancel7x =5346 {cm}^{3} \\ \sf \: \to \: \:198 {x}^{3} = 5346 {cm}^{3} \\ \sf \to \: x^3 = \frac{5346}{198} \\ \bf\to \: x^3 = 27 \\ \bf \to x = 3\sqrt{27} \\ \bf \to x = 3$

Therefore,

Radius = 3x = 3 × 3 = 9cm.

Height = 7x = 7 × 3= 21cm.