Question

(25) The Curved Surface area of a Cylinder is 4400 lm?
and the Circumference of its base is 110cm. Find
the volume of Cylinder​

Answer 1

Step-by-step explanation:

Curved surface area of cylinder =2πrh

Circumference of the base =2πr

ATP,

2πr=110

$2 \times \frac{22}{7} \times r = 110$

$\frac{44}{7} \times r = 110$

$r = 110 \times \frac{7}{44}$

$r = \frac{35}{2}$

therefore,

2πrh=4400

$2 \times \frac{22}{7} \times \frac{35}{2} \times h = 4400$

$22 \times 5 \times h = 4400$

$h = \frac{4400}{110}$

$h = 40$

Radius of cylinder = 35/2 cm

Height of a cylinder = 40cm.

$volume \: of \: a \: cylinder = \pi {r}^{2} h \: cubic \: unit$

$= \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} \times 40 \: cubic \: cm$

$= 55 \times 20 \times 35 \: cubic \: cm$

$= 38500 \: cubic \: cm$

Answer 2

Answer :

›»› The volume of cylinder is 38500 cm³.

Given :

• Curved surface area of a cylinder = 4400 cm².
• Circumference of cylinder base = 110 cm.

To Find :

• Volume of a cylinder = ?

How to solve?

Here, in this question we have to find the volume of a cylinder, So, firstly we need to find the radius of a cylinder, after that we will find the height of a cylinder, after all this we will find the volume of a cylinder on the basis of conditions given above.

To find the radius of a cylinder, we use the formula of circumference of a cylinder base.

To find the height of a cylinder, we use the formula of curved surface area of cylinder.

To find the volume of a cylinder, we use the formula of volume of cylinder.

Solution :

Finding the radius of a cylinder.

As we know that

→ Circumference of cylinder base = 2πr

→ 110 + 2 * 22/7 * r

→ 110 * 7 = 2 * 22 * r

→ 770 = 2 * 22 * r

→ 770 = 44 * r

→ 770 = 44r

→ r = 770/44

→ r = 35/2

→ r = 17.5

The radius of a cylinder is 17.5 cm.

Finding height of a cylinder.

As we know that

→ CSA of a cylinder = 2πrh

→ 4400 = 2 * 22/7 * 17.5 * h

→ 4400 * 7 = 2 * 22 * 17.5 * h

→ 30800 = 2 * 22 * 17.5 * h

→ 30800 = 44 * 17.5 * h

→ 30800 = 770 * h

→ 30800 = 770h

→ h = 30800/770

→ h = 3080/77

→ h = 40

The height of a cylinder is 40 cm.

Now,

Finding the volume of a cylinder.

As we know that

→ Volume of cylinder = πr²h

→ Volume of cylinder = 22/7 * (17.5)² * 40

→ Volume of cylinder = 22/7 * 17.5 * 17.5 * 40

→ Volume of cylinder = 22/7 * 306.25 * 40

→ Volume of cylinder = 22 * 43.75 * 40

→ Volume of cylinder = 962.5 * 40

→ Volume of cylinder = 38500

Hence, the volume of cylinder is 38500 cm³.