Question

A sphere, a cylinder and a cone are of the same radius, where a cone and cylinder are of same height and radius. Find the ratio of their curved surface areas.
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Answer 1

Answer:

4:4:√5

Step-by-step explanation:

as we know he 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)+(2r²)  =  √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

hope it help's u ....... good day !

Answer 2

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= (r2+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

2

:4πr

2

:πr

2

5

=4:4:

5