Find the values and arrange in increasing order:
(A) If each edge of a cube is increased by 20%, then the percentage increase in its volume is:
(B) If the radius of a cylinder is increased by 20%, while height increase 10%, then the percentage increase in the volume of the cylinder:
(C) If each edge of a cube is increased by 20%, then the percentage increase in its surface area is:
(D) If the radius of a sphere is increased by 10%, then the percentage increase in its volume is:
Choose the correct order:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (D), (C), (B), (A)
To find the correct order, let's calculate the percentage increase for each case:
(A) Cube Edge increased by 20% (Volume)
- Original Volume $V = a^3$
- New Edge $= 1.2a$
- New Volume $= (1.2a)^3 = 1.728a^3$
- Increase $= (1.728 - 1) \times 100 =$ $72.8\%$
(B) Cylinder Radius +20%, Height +10% (Volume)
- Original Volume $V = \pi r^2 h$
- New Radius $= 1.2r$, New Height $= 1.1h$
- New Volume $= \pi (1.2r)^2 (1.1h) = \pi (1.44r^2)(1.1h) = 1.584 \pi r^2 h$
- Increase $= (1.584 - 1) \times 100 =$ $58.4\%$
(C) Cube Edge increased by 20% (Surface Area)
- Original Surface Area $S = 6a^2$
- New Edge $= 1.2a$
- New Surface Area $= 6(1.2a)^2 = 6(1.44a^2) = 1.44 (6a^2)$
- Increase $= (1.44 - 1) \times 100 =$ $44\%$
(D) Sphere Radius increased by 10% (Volume)
- Original Volume $V = \frac{4}{3} \pi r^3$
- New Radius $= 1.1r$
- New Volume $= \frac{4}{3} \pi (1.1r)^3 = 1.331 \left(\frac{4}{3} \pi r^3\right)$
- Increase $= (1.331 - 1) \times 100 =$ $33.1\%$
Increasing Order: (D), (C), (B), (A)