Question

pls tell me the answer and explain me

Answer 1

Answer : 4th Option : 4:4:√5,

Explanation :

Given that radius and Height are equal for all,

So,

Let Radius be r,
and height be h,

Curved surface areas formulas :

(1) For sphere : 4πr²,
(2) For cylinder : 2πrh,
(3) For cone : πrl,

Radius of Sphere = r = radius of Cylinder = r = Radius of Cone,

Now, Here is the main point to be remembered,

Height of Sphere = Diameter of Sphere,

=> Height of Sphere = 2r,

According to the question,

We can say that,
Height of Cone and cylinder are also 2r,

Now,
l (Slant Height ) = √(r²+h²)

=> l = (√5)r [I skipped the process]

Substituting all the values we have,

=> C.S.A of Sphere = 4πr²,

=> C.S.A of cylinder = 2πr*2r = 4πr²,

=> C.S.A of Cone = πr * √5 * r = √5 *πr²,

Ratio of C.S.A of them is,

4πr² : 4πr² : √5πr²,

Cancelling πr² on all sides,

=> Ratio is 4:4:√5,

Therefore : The ratio of C.S.A of Sphere , C.S.A of cylinder, C.S.A of Cone is 4:4:√5,

Hope you understand, Have a Great day !..
Thanking you, Bunti 360 !.