Question

A solid metallic cylinder height 15 cm radius 9 cm is melted to make two cones in the ratio of volume 3:4 and of the same height 10 cm what is the percent increase in the curved surface area?​

Answer 1

Change in curved surface are is 95 %

Step-by-step explanation:

Volume of solid metallic cylinder = πr²h

                                                      = $\frac{22}{7}.9.9.15$ = 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 = $\frac{972\pi-49\pi }{972\pi }$

                                                     = 95%