NTSE Stage 2 SAT 2019 Exam Question Paper

Question : 49 of 100

Marks: +1, -0

A solid metallic cylinder of height 10 cm and diameter 14 cm is melted to make two cones in the proportion of their volumes as

3:4

, keeping the height 10 cm, what would be the percentage increase in the flat surface area?

Solution:

Let

r_1

and

r_2

be the radii of two cones.
Volume of cylinder = Sum of volume of two cones

π×7^{2}×10=\;\;{π}/{3}×10(r_{1}^{2}+r_{2}^{2})

⇒r_{1}^{2}+r_{2}^{2}=49×3

......(1)
∴ Percentage increase

=\;\;{πr_{1}^{2}+πr_{2}^{2}-2π×7^{2}}/{2×π×7^{2}}×100

=\;\;{r_{1}^{2}+r_{2}^{2}-2×49}/{2×49}×100

=\;\;{(49×3-49×2)}/{49×2}×100

[From(1)]

=50%

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