Question

The total surface of a right circular cone of slant height 17 cm Is 200pie cm2 . Calculate it radius.If this cone is melted and formed into solid sphere of radius 2cm ,find the no of sphere formed.

Answer 1

Answer:

Given Surface area= 200πcm ²

Slant. height = 17cm

No of Sphere Formed =64

Step-by-step explanation:

Total surface area of cone =πr²+πrl

200πcm²=πr²+πrl

200πcm²=π(r²+rl)

200cm²= r²+rl

200cm²= r²+17r

r²+17r-200=0

On solving the quadratic equation

r²+25r-8r-200=0

r(r+25)-8(r+25)=0

(r+25) (r-8) =0

Radius= -25cm, 8cm

Neglecting Negative Value -25

Radius Obtained= 8cm

Volume of Sphere with 8cm

Volume of sphere= 4/3πr³

Volume of Sphere = 4/3×π×(8)³

Volume of Sphere=. 2048/3πcm³--(1)

Volume of Sphere with Radius 2cm

4/3πr³=4/3π×(2)³cm= 32/3πcm³--(2)

On comparing equation 1 and 2

2048/3πcm³= 32/3πcm³

we get

64 =No of the sphere formed