Question
Download Solution PDFThe length, breadth and height of a room in the shape of a cuboid are increased by 20%, 25% and 30% respectively. Find the percentage
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Length increase = 20%
Breadth increase = 25%
Height increase = 30%
Formula Used:
Percentage increase in volume = [(New volume - Original volume) / Original volume] × 100
Calculation:
Let the original dimensions of the cuboid be:
Length = L, Breadth = B, Height = H
Original Volume = L × B × H
After the increase, the new dimensions will be:
New Length = L × (1 + 20/100) = 1.20L
New Breadth = B × (1 + 25/100) = 1.25B
New Height = H × (1 + 30/100) = 1.30H
New Volume = 1.20L × 1.25B × 1.30H = 1.95 × L × B × H
Percentage increase in volume = [(1.95 × L × B × H - L × B × H) / (L × B × H)] × 100
⇒ Percentage increase in volume = [(1.95 - 1) × 100] = 0.95 × 100 = 95%
∴ The percentage increase in the volume of the cuboid is 95%.
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