1.

A sphere has the same curved surface area as a cone of vertical height 40 cm and radius 30 cm. The radius of the sphere is 1). 5√5 cm2). 5√3 cm3). 5√15 cm4). 5√10 cm

Answer»

Let the radius of Sphere be r cm

Then CSA of sphere is 4πr2

If R is the radius of cone and ‘L’ is the slant HEIGHT then CSA of cone = πRl

l = √(R2 + h2) = √(302 + 402) = 50 cm

Given CSA of Sphere = CSA of cone

4 × π × r2 = π × 30 × 50

⇒ r2 = 15 × 25 = 375

∴ r = 5√15 cm


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