Question

A solid metallic cylinder of height 15 cm and radius 9 cm is melted to make two cones in the ratio of volume 3: 4 and of same height as 10 cm. What is the percentage increase in the flat surface area?​

Answer 1

Answer:

Change in curved surface are is 95 %

Step by step explaination:

Volume of solid metallic cylinder = πr²h

= \frac{22}{7}.9.9.15

7

22

.9.9.15 = 3818.6 cm³

Surface area of flat surface of cylinder = 2πr²

= 972π

Now this cylinder is recast into two cones in the ration 3:4 , So , the volume of two cones is 660 cm³ and 880 cm³.

Let the radii of two cones be R₁ and R₂

πR₁² = 66 and πR₂² = 88

R₁² = 21 and R₂² = 28

Therefore, πR₁² = 21π and πR₂² = 28π

Combined surface area of flat surface of both cones = 21π + 28π = 49 π

Change in curved surface area = \frac{972\pi-49\pi }{972\pi }

972π

972π−49π

= 95%