If all three dimensions of a cuboid are increased by 10%, the volume increases by what percentage?

Correct — D. Volume = length × breadth × height, so each 10% rise is a × 1.1 multiplier.

Multiplier per dimension = 1 + 10⁄100 = 1.1
Two dimensions: 1.1 × 1.1 = 1.21
Third dimension: 1.21 × 1.1 = 1.331

Increase = 1.331 − 1 = 0.331 = 33.1% → option (d)

Why the others are wrong

• (a)
  10% — 10% is the change in one length. Volume multiplies three lengths, so the 10% compounds three times: 1.1³ = 1.331.
• (b)
  21% — 21% is 1.1² = 1.21, the change for two dimensions, such as the area of the base. The height rises too, adding another × 1.1.
• (c)
  30% — 30% adds 10 + 10 + 10. Percentage changes multiply, and adding them drops the cross terms, 3 × 1% + 0.1% = 3.1%.

Scaling every length of a solid by a factor k scales its volume by k³ and its surface area by k².

With k = 1.1, area becomes × 1.21 (+21%) and volume × 1.331 (+33.1%).

The shortcut for two successive changes of a% and b% is a + b + ab⁄100. Here 10 + 10 + 1 = 21%, then 21 + 10 + 2.1 = 33.1%.

Key facts

• If every length is multiplied by k, volume is multiplied by k³ and area by k².
• 1.1² = 1.21 and 1.1³ = 1.331.
• Two successive changes of a% and b% give a net change of a + b + ab⁄100 percent.

Common traps

• Adding the three 10% rises to 30% instead of compounding them.
• Stopping at 1.1² = 1.21 and answering 21%, which covers two of the three dimensions.

No directly related past PYQ was found.