Question

.a sphere a cylinder and a cone are the same radius and same height find the radius of their curved surface areas and volumes​

Answer 1

Let r be the common radius of a cylinder, cone and a sphere.

Then, height of the cylinder = Height of the cone = Height of the sphere

= 2r

Let 'I' be the slant height of the cone. Then

l = root under(√r2 + h2) = root under(√r2 + (2r) = √5r

Also, S1 = Curved surface area of cylinder = 2πrh = 2πr. 2r = 4πr2

S2 = Curved surface area of cone = πrl = πr√5r = √5πr2

S3 = Curved surface area of sphere = 4πr2

Now, S1 : S2  :S3 = 4πr2 : √5πr2 : 4πr2  

∴  S1 : S2 : S3 = 4 : √5 : 4

he Ratio of the volumes of a cylinder, a cone and a sphere is 3 : 1 : 2.