Question

15 d) A cylindrical tank has two hemisphere
as its two ends the length of axis at its
centre is 11 mts and radius of a hemisphere!
is 3.5cm Then find the capacity of the
tank in liters​

Answer 1

Answer :-

Capacity of tank = 42.35 litres

$\rule{50}2$

Given:-

• Length (height of cylinder) = 11 m
• Radius of hemisphere and cylinder = 3.5 cm

Find:-

Capacity of the tank.

Solution:-

A cylindrical tank has two hemispheres at its two ends and length of the cylinder is 11 m (1100 cm)

Also, given that the radius of the hemisphere is 3.5 cm.

As hemispheres are joined at the ends of the cylinder. Means, the radius of the cylinder and hemisphere is same i.e. 3.5 cm.

Now,

Volume of cylinder = πr²h and Volume of hemisphere = 2/3πr³

So,

Capacity of tank = Volume of cylinder + Volume of two hemispheres

Let the -

• the capacity of tank be x

→ x = πr²h + 2 × 2/3πr³

→ x = πr²(h + 2 × 2/3r)

→ x = 22/7 × (3.5)² (1100 + 4/3 × 3.5)

→ x = 22/7 × 12.25 (1100 + 14/3)

→ x = 22/7 × 12.25 (1100 + 4.67)

→ x = 269.6/7 (1104.67)

→ x = 38.5(1104.67)

→ x = 42354.67 cm

To convert cm into litres. Divide the value by 1000

→ x = 42354.67/1000

→ x = 42.35 (approx.)

•°• Capacity of the tank is 42.35 lit.

Answer 2

Solution: Volume of object = It's Capacity

→ Volume of cylinder + 2 Volume of hemispheres.

Volume of cylinder = πr²h

Volume of hemisphere = ⅔ πr³

→ πr²h + 2(⅔)πr³

→ πr²h + 4πr³/3

→ πr²(h + 4r/3)

→ π × 3.5² × (1100 + 4/3 × 3.5)

→ 22/7 × 3.5 × 3.5 × (1100 + 14/3)

→ 22 × 0.5 × 3.5 × (3300 + 14)/3

→ 38.5 × 3314/3

→ 42530 cm³

Now 1 cm³ = 1000 liters

Capacity = 42530/1000 l

→ 42.5 liters

Answer: Capacity is 42.5 liters