Question

a cone of height 24 cm and radius of base 6cm is made in a sphere.find radius of sphere​

Answer 1

Answer:

Definition :

A cone is a three-dimensional geometric shape. It is formed by line segments, half lines or lines connecting at the apex.

Given:–

Height of cone(h) =24 cm

Radius of base(r) =6 cm

Slant height of cone (l)

=(h²+r²) ^1 /2

=(24²+6²)^1 /2

=(576+36)^1 /2

=(612)^1 /2

=24.73 cm ... {Approx}

Now, As Volume of the cone(V) is ¶*r²*h/3.

Therefore,

V=3.14*6²*24/3

V=3.14*36*8

V=904.32 cm³

And now on solving for the sphere,

Volume of sphere is 4/3*¶*r³.

Hence on solving further,

4/3¶r³=904.32 cm³

¶r³=904.3*3/4

22/7*r³=904.3*3/4

r³=904.3*3/4*7/22

r³=904.3*21/88

r³=215.79

r=(215. 79)^1 /3

r=5.99=>6 cm approximately

Therefore the radius of the sphere is 6 cm approximately.