Question

A rectangular tank 15 m long and 11 m broad is required to receive entire liquid contents from a fully cylindrical tank of internal diameter 21 m and length 5 m. Find the least height of the tank that will serve the purpose.

Answer 1

Answer:

The least height of the tank is 10.5 m.

Step-by-step explanation:

Given :  

Length of the rectangular tank , l = 15 m

Breadth of the rectangular tank , b = 11 m

Height of the cylindrical tank , H = 5m  

Diameter of the cylindrical tank = 21

Radius of the cylindrical tank, r  = 21/2 m = 10.5 m

Let the height of the rectangular tank be = h m

Volume of the rectangular tank = length × breadth ×  height = lbh

Volume of the rectangular tank = 15 × 11× h m³ …………………………. (1)

Volume of the cylindrical tank = πr²H = π × 10.5² × 5 ……………………………(2)

Since, rectangular tank receive entire liquid contents from a full cylindrical tank so their volumes are equal.

Volume of the rectangular tank = Volume of the cylindrical tank

15 × 11× h m³ = π × 10.5² × 5

[From eq 1 & 2]

165 h = 22/7 × 10.5 × 10.5  × 5

165 h = 22 × 1.5 × 10.5  × 5

165h = 165 × 10.5  

h = (165 × 10.5 )/165

h = 10.5 m

Hence, The least height of the tank is 10.5 m.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Step by step explanation :

Let the height of the rectangular tank = h.

As per the question,

Length of the tank = 15 m

Breadth of the tank = 11 m

Now,

Length of cylindrical tank = 5 m

Radius of cylindrical tank = 21/2m

( Radius = d / 2 )

Now ,

To find out the least height of the tank, we need to equate the volume of two tanks.

So,

15 × 11 × h=π × (21/2)^2×5

h=22/7 × 21/2 × 21/2 × 5/15 × 1/11

h=21/2

h=10.5 metres

Hence, the least height of the tank = 10.5 metres.