Question

the curved surface area of a cylinder is 4620cm². if it's height is 21cm, find the circumference and the area of its base​

Answer 1

Solution!!

Given:-

→ Curved surface area (CSA) = 4620 cm²

→ Height = 21 cm

To find:-

→ Circumference

→ Area of its base

We know the CSA and the height. Using these, we can find out the radius. Let's find the radius first.

→ CSA = 2πrh

→ 4620 cm² = $\sf 2\times \dfrac{22}{7}\times r\times 21\:cm$

→ 4620 cm² = 2 × 22 × 3 cm × r

→ 4620 cm² = 132 cm × r

→ r = 4620 cm² ÷ 132 cm

→ r = 35 cm

We have the radius now. All we have to do is put the value of the radius in the formulae to find the circumference and the area. Let's find out the circumference first.

→ Circumference = 2πr

→ Circumference = $\sf 2\times \dfrac{22}{7}\times 35\:cm$

→ Circumference = 2 × 22 × 5 cm

→ Circumference = 220 cm

Now, let's find out the area of the base.

→ Area = πr²

→ Area = $\sf \dfrac{22}{7}\times 35\:cm\times 35\:cm$

→ Area = 22 × 5 cm × 35 cm

→ Area = 3850 cm²

Answer 2

$\huge\bold{Answer:-}$

Given:-

• The curved surface area of a cylinder is 4620 cm² .
• The height of the cylinder is 21 cm.

To Find:-

• The circumference of the cylinder .
• The area of its base .

Solution:-

we know ,

The curved surface area of a cylinder = 2πrh square unit.

where,.

r = radius of the cylinder

h = height of the cylinder .

Now , we have to find the radius of the cylinder by using the curved surface formulla.

As height = 21 cm ( given)

curved surface area = 4620 cm²

let, the radius be r cm

ATQ

➾ 2πrh = 4620

➱ 2 × $\dfrac{22 } {7}$ × r × 21 = 4620

➱ 2 × 22 × r × 3 = 4620

➱ r = $\dfrac{4620} {2 × 22 × 3}$

➱ r = 35 cm

Therefore , The radius of the cylinder is 35 cm .

Now ,

The circumference of the base = 2πr unit.

So , Radius of the cylinder = Radius of the base .

Radius = 35 cm

➾ Circumference = 2πr

➱ 2 × $\dfrac{22} {7}$ × 35 cm

➱ 2 × 22 × 5 cm

➱ 220 cm .

Therefore , The circumference of the base is 220cm .

now,

.

The Area of the base = πr² square unit .

Radius of the base = 35 cm

➾ Area = πr²

➱ $\dfrac{22 } {7}$ × 35 × 35 cm²

➱ 22 × 5 × 35 cm²

➱ 3850 cm²

Therefore , The area of the base is 3850 cm² .