A cylindrical drum of radius 14cm contains water. A solid cuboid having length 14cm, breadth 11cm, height 12cm is dropped in the water. Find the increase in the water level of the tank?
Answers
EXPLANATION.
Cylindrical drum of radius = 14 cm.
Solid cuboid having length 14cm, breadth 11cm, height 12cm.
As we know that,
Formula of :
Volume of cylinder = πr²h.
Volume of cuboid = L x B x H.
Volume of cylinder = Volume of cuboid.
⇒ πr²h = L x B x H.
⇒ (22/7) x 14 x 14 x h = 14 x 11 x 12.
⇒ 22 x 14 x 14 x h = 14 x 11 x 12 x 7.
⇒ 22 x 14 x h = 11 x 12 x 7.
⇒ 2 x 14 x h = 12 x 7.
⇒ 2 x 2 x h = 12.
⇒ 4 x h = 12.
⇒ h = 3 cm.
Increases in the water level of the tank = 3 cm.
MORE INFORMATION.
(1) = Volume of cuboid = L x B x H.
(2) = Volume of cube = a³.
(3) = Volume of cylinder = πr²h.
(4) = Volume of cone = 1/3πr²h.
(5) = Volume of sphere = 4/3πr³.
(6) = Volume of hemisphere = 2/3πr³.
Question:-
A cylindrical drum of radius 14cm contains water. A solid cuboid having length 14cm, breadth 11cm, height 12cm is dropped in the water. Find the increase in the water level of the tank?
Required Answer:-
Given:-
- Radius of the cylindrical drum = 14cm
- Length, breadth and height of the solid cuboid is 14cm, 11cm and 12cm respectively.
To Find:-
- The increase level in the water of the tank.
Solution:-
We know that:-
- Volume of a cylinder = πr²h
- Volume of cuboid = LBH
We were given,
- Radius of the cylinder r = 14cm.
- Length of the solid cuboid L = 14cm
- Breadth of the solid cuboid B = 11cm
- Height of the solid cuboid H = 12cm
According to the question:-
Volume of the cylindrical drum = Volume of the solid cuboid
=> πr²h = LBH
=> 3.1416 × (14)² × h = 14 × 11 × 12
=> 3.1416 × 196 × h = 1848
=> h = 1848/(3.1416 × 196)
∴ h = 3.001cm → 3cm
Hence, the increase level in the water of the tank is 3cm