Question

The cylinder and sphere have the same radius (r) and the same height. Calculate the ratio of their volume.

Answer 1

Since, the height of a sphere is the diameter, the cone and cylinder have height 2r.

Then Curved surface area of Sphere= 4πr²

Curved surface area of cylinder = 2πr(2r) = 4πr²

Curved surface area of cone = πrl

where, l = √(r2 + h2 ) = √( r2 + (2r)2) = √(5r2) = r√5

⇒ Curved surface area of cone = π√5r2

Now,

Ratio of CSA 's a sphere ,cylinder and a cone = 4πr2:2πrh : πrl

= 4πr2:4πr2 : πr2√5

= 4 : 4 : √5

Answer 2

Step-by-step explanation:

volume of Sphere having radius R =4/3 pie r^2

volume of cone having radius r =pie r^2 h/3

and height H .

=4/3pie r^2 = pie r^2h/3

=4r = h

=r/h =1/4

so,

r:h is1:4

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