Question

The curved surface area of a cone is 20cm^2 and its slant height and radius are consecutive natural no.s then find its volume​

Answer 1

Answer:

eyrhy6jy746

Step-by-step explanation:

dbahut484tecbdjyfvehejhwthxf

Answer 2

Answer:

16 π cm³

Step-by-step explanation:

There is correction in question:- The curved surface area of a cone is 20π

Let the slant height be x+1 & radius be x.

Now, curved surface area of a cone = 20π

∴ π × radius × slant height = 20π

∴ π. x+1. x = 20π

∴  (x² + x) = 20

∴ x² + x - 20 = 0

∴ x² + 5x - 4x -20 = 0

∴ x(x + 5) -4 (x +5) = 0

∴ (x - 4) (x + 5) = 0

Therefore x =  4 or -5

x = -5 is invalid.

So, x = 4

So, Radius = 4, Slant Height = 5

Since Slant Height = 5, Height = √(5² - 4²) = 3

Volume = 1/3 πr²h = 1/3. π. 4².3  = 16 π cm³