Question

A cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water level in the tank.

Answer 1

Hint: Water is poured from the cylindrical bucket to the rectangular tank. And the bucket is full of water. So the volume of water is equal to the volume of the bucket. To find the height of water level in the tank, equate the volume of the cylindrical bucket with the volume of the tank and substitute the given values.
Formulas used:
Volume of a cylinder is $ \pi {r^2}h $ , where r is the base radius of the cylinder and h is the height of the cylinder.
Volume of a cuboid (rectangular tank) is $ l \times b \times h $ , where l is the length, b is the breath and h is the height of the cuboid.

Complete step-by-step answer:
We are given that a cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide.
We have to find the height of the water level in the tank.

Volume of water in the cylindrical bucket is $ \pi {r^2}h $
The length of diameter is 28 cm and the radius is half the diameter, which is 14 cm.
 $
  Volum{e_{bucket}} = \pi {r^2}h \\
  \pi = \dfrac{{22}}{7},r = 14,h = 72 \\
   \Rightarrow Volum{e_{bucket}} = \dfrac{{22}}{7} \times 14 \times 14 \times 72 \\
  \therefore Volum{e_{bucket}} = 44352c{m^3} \\
  $
Volume of a rectangular tank with water is $ l \times b \times h $
 $
  Volum{e_{tank}} = l \times b \times h \\
  l = 66cm,b = 28cm,h = ? \\
   \Rightarrow Volum{e_{tank}} = 66 \times 28 \times h \\
  \therefore Volum{e_{tank}} = \left( {1848h} \right)c{m^3} \\
  $
The volume of the water in the rectangular tank is the volume of the cylindrical bucket.
 $
  Volum{e_{tank}} = Volum{e_{bucket}} \\
   \Rightarrow 1848h = 44352 \\
   \Rightarrow h = \dfrac{{44352}}{{1848}} \\
  \therefore h = 24cm \\
  $
Therefore, the height of the water level in the rectangular tank is 24 cm.

Note: A cuboid is a three dimensional shape with 6 faces, 8 vertices and 12 edges. A cube is also a three dimensional shape which has 6 faces, 8 vertices and 12 edges. But all the edges are equal in a cube but not in a cuboid. The areas and volumes of cube and cuboid are different. So do not confuse a cube with a cuboid.