The radius of the sphere whose surface area is the same as cylinder is 2.03 meters.
Let R be the radius of the sphere.
According to the given question.
The height of the cylinder is 4 meters
Radius of the cylinder is 1.5meters
The formula for the surface area of cylinder is given by
Surface area of cylinder = 2πrh + 2πr^2
Where r is the radius of the cylinder and h is the height of the cylinder.
So, the surface area of the cylinder whose height is 4 meters and radius is 1.5 meters
= 2πr( h + r)
= 2π(1.5)(4 + 1.5)
= 16.5π
Thereofore,
The radius of the sphere whose surface area is the same as cylinder is given by
4πR^2 = 16.5π
⇒ 4R^2 = 16.5
⇒ R^2 = 4.125
⇒ R = √4.125
⇒ R = 2.03 meters
Hence, the radius of the sphere whose surface area is the same as cylinder is 2.03 meters.
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