XAT 2015 — QA & DI Question 6
A solid metal cylinder of 10 cm height and 14 cm diameter is melted and re-cast into two cones in the proportion of 3 : 4 (volume), keeping the height 10 cm. What would be the percentage change in the flat surface area before and after?
Answer & solution
- A
9%
- B
16%
- C
25%
50%
- E
None of the above
Flat surface area of the cylinder = 2 × π × 72 = 98 π cm2
Volume of the cylinder = π × 72 ×10
= 490 π cm3
Volume of cone A = (3/7) × 490 π = 210 π cm3 = (1/3) × flat surface area of cone
A × 10
Flat surface area of cone A = 63 π cm2
Volume of cone B = (4/7) × 490 π = 280 π cm3 = (1/3) × flat surface area of cone
B × 10
Flat surface area of cone B = 84 π cm2
Total flat surface area of cones
= (63 + 84) π = 147 π cm2
Percentage change in the flat surface area
= (147 – 98)/98 × 100 = 50%
Hence, option (d).âââââââ