Question

the circumference of the base of a cylindrical vessel is 132cm and height is 25cm how many litres of water can it hold (1000cm3=1 L)​

Answer 1

Given :

The circumference of the base of a cylindrical vessel is 132cm and height is 25 cm.

To FinD :

How many litres of water can it hold?

Solution :

Analysis :

Here the formula of volume of cylinder is used. First we have to find the radius with the help of the circumference of the cylinder. To find the capacity we need to find the volume. Using the radius and height we can find the volume and then by using the volume we can find the capacity in litres.

Required Formula :

• Circumference of cylinder = 2πr

• Volume of Cylinder = πr²h

where,

• π = 22/7
• r = radius
• h = Height

Explanation :

Let the radius be "r" cm.

We know that if we are provided with the circumference is asked to find the radius then our required formula is,

Circumference of cylinder = 2πr

where,

• π = 22/7 or 3.14
• r = r cm
• Circumference = 132 cm

Using the required formula and substituting the required values,

⇒ Circumference of cylinder = 2πr

⇒ 132 = 2 × 22/7 × r

⇒ 132 = 44/7 × r

⇒ 132 × 7/44 = r

⇒ 924/44 = r

⇒ 21 = r

∴ Radius = 21 cm.

Now the volume :

We know that if we are provided with the radius and height is asked to find the capacity then our required formula is,

Volume of Cylinder = πr²h

where,

• π = 22/7 or 3.14
• r = 21 cm
• h = 25 cm

Using the required formula and substituting the required values,

⇒ Volume of Cylinder = πr²h

⇒ Volume of Cylinder = 22/7 × 21 × 21 × 25

⇒ Volume of Cylinder = 22 × 3 × 21 × 25

⇒ Volume of Cylinder = 34650

∴ Volume of Cylinder = 34650 cm³.

Now the conversion :

We know that,

1000 cm³ = 1 L

So,

⇒ 34650 cm³ = 34650/1000

= 34.65 L

The vessel can hold 34.65 Litres water.