Question

3. A sphere, a cylinder and a cone are of
the same radius and came helight. Find
the ratio of their curved surface areas​

Answer 1

Answer:

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=

(r

2

+h

2

)=

(r2+(2r)

2

)=

5r

2

=r

5

⇒ Curved surface area of cone =π

5r

2

Now,

ratio of CSA 's a sphere ,cylinder and a cone = 4πr

2

:2πrh:πrl

=4πr(sq):4πr(sq) :πr(sq)✓5

=4:4: 5