Question

9. Water from a cylindrical water tank of height 10.5 m and a base with diameter 4.2 m is emptied
into a cuboidal water tank of dimensions 15 mx 7 mx 6 m. Find the height of water in the cuboi-
dal water tank.​

Answer 1

Given,

Water from a cylindrical water tank of height 10.5 m and a base with diameter 4.2 m is emptied  into a cuboidal water tank of dimensions 15 mx 7 mx 6 m.

To Find,

The height of the water in the cuboidal tank.

Solution,

→ First we have to find the volume of the cylindrical tank.

Height = 10.5 m

Diameter = 4.2 m

So, radius = $\dfrac{4.2}{2}$ = 2.1 m

Volume = πr²h

= $\dfrac{22}{7}\times2.1\times2.1\times10.5$

= 145.53 m³

→ The base area of the cuboidal tank

Length = 15 m

Breadth = 7 m

Area = lb

= 15 x 7

= 105m²

→ Height of the water in the cuboidal tank

Height = Volume ÷  Base Area

Height = 145.53 ÷ 105

= 1.386 m

∴ The height of the water in the cuboidal tank is 1.386 m.

Answer 2

☞Correct Question:

Water from a cylindrical water tank of height 10.5m and a base with diameter 4.2m is emptied into a cuboidal water tank of dimensions 15m x 7m x 6 m. Find the height of water in the cuboidal water tank.

☞Required Answer:

The height of water in Cuboidal water tank is 1.386m.

☞Solution:

Given:

•Hight of cylindrical tank = 10.5m

•Diameter of cylindrical tank = 4.2m

•Length of cuboidal tank = 15m

•Breadth of cuboidal tank = 7m

•Height of cuboidal tank = 6m

To find:

Height of water in cuboidal tank ?

☞How to solve:

Height of cylindrical tank = 10.5m

Diameter of cylindrical tank,D = 4.2m

Radius of cylindrical tank = $\sf\dfrac{D}{2}$

= $\sf\dfrac{4.2}{2}$

= 2.1m

✒Volume of cylinder = πr²h

= $\sf\dfrac{22}{7}$ × 2.1 × 2.1 × 10.5

= 145.53m³.

✩Therefore, volume of cylindrical tank = 145.53m³

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Length of cuboidal tank, l = 15m

Breadth of cuboidal tank, b = 7m

✒Area of cuboidal tank = l×b

= 15 × 7

= 105m².

✩ Therefore Area of cuboidal tank = 105m²

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✒Height of water in cuboidal tank = ?

=> Height of water = $\sf\dfrac{Volume\:of\:Cylinder}{Area\:of\:Cuboid}$

= $\sf\dfrac{145.53}{105}$

= 1.386m

✩Therefore, Height of water = 1.386m.

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