A fish tank is in the shape of cuboid. Shyam who wants to increase the volume of the tank so as to have more fish, increased the length, width and depth of the tank by 10%, 15% and 20% respectively. By what percent has the tank's volume increased?

Ques. A fish tank is in the shape of cuboid. Shyam who wants to increase the volume of the tank so as to have more fish, increased the length, width and depth of the tank by 10%, 15% and 20% respectively. By what percent has the tank's volume increased?

A) 46.2%

B) 33.1%

C) 51.8%

D) 62.0%

Ans. C) 51.8%

Explanation: 

Volume of cuboid = l × b × h

Suppose the volume of cuboid is unity i.e., 1 

Change in volume = New volume - Original volume

Let's find out new volume

According to the question, length is increased by 10%, width is increased by 15% and depth/height is increased by 20% 

New length = l + l × 10% = 1.1 l

New width = w + w × 15% = 1.15 w 

New depth = d + d × 20% = 1.2 d

 

Since l×b×h = 1 

Therefore new volume = 1.518 m³

Change in volume = 1.518 - 1 = 0.518m³

∆ in volume %age 

= (∆ in volume)/ Original volume × 100

= 0.518/1 × 100

= 51.8% Ans

Thus the volume of fish tank has increased by 51.8%.