The length breadth and height of a cuboid are increased by 10%, 20% and 50% respectively. What is the percentage increase in volume of the cuboid?

Correct option is C

Given:

Initial Length (L) = L

Initial Breadth (B) = B

Initial Height (H) = H

Length increased by 10%

Breadth increased by 20%

Height increased by 50%

Concept:

The volume of a cuboid is given by the product of its length, breadth, and height.

Formula Used:

Volume of cuboid = Length × Breadth × Height

Solution:

Initial Volume (V_initial) = L × B × H

New Length (L_new) = L × (1 + 10/100) = 1.1L

New Breadth (B_new) = B × (1 + 20/100) = 1.2B

New Height (H_new) = H × (1 + 50/100) = 1.5H

New Volume (V_new) = L_new× B_new× H_new

V_new= 1.1L × 1.2B × 1.5H

V_new= 1.98LBH

Percentage Increase in Volume = [(V_new- V_initial)/V_initial] × 100

=> Percentage Increase = [(1.98LBH - LBH)/LBH] × 100

=> Percentage Increase = [0.98LBH/LBH] × 100

=> Percentage Increase = 0.98 × 100

=> Percentage Increase = 98%

Hence, the percentage increase in volume of the cuboid is 98%.