SSC CGL 9 Aug 2017 Shift 1 Paper

Question : 53 of 100

Marks: +1, -0

Three solid spheres of radius 3 cm, 4 cm and 5 cm are melted and recasted into a solid sphere.
What will be the percentage decrease in the surface area?

Validate

Solution:

According to the question,

4/3π(3)^3+4/3π(4)^3+4/3π(5)^3=4/3πr^3

⇒

27 + 64 + 125 = r^ 3

⇒

216 = r ^3 ⇒ r = √^3 {216}

∴ r = 6
The surface area of all three spheres

= 4π(3)^2 +4π(4)^2 +4π(5)^2

= 4π × 9 + 4π × 16 + 4π × 25

= 200π
The surface area of new sphere

= 4 π(6)^2 =144π

∴ Required decrease

={200π-144π}/{200π} ×100=28%

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