The surface area of a solid metallic sphere is 616 cm sq . it is melted and recast into a cone of height 28cm . Find the diameter of the base of the cone so formed. ( use π = 22/7 ).
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Given that :
Surface area of Solid metallic sphere = 616 cm^2
And the height of Melted cone = 28 cm.
Now, as we know that :
Total Surface Area of sphere = 4πr^2
=> 616 = 4 × 22/7 × r^2
=> r^2 = 49 => r = 7 cm.
So, the radius of the sphere is 7 cm.
We know that :
Volume of Sphere = 4/3 πr^3
And volume of cone = 1/3 πr^2h
After melting the volume will be the same
ATQ :
4/3 πr^3 = 1/3 πr^2h
=> 4r = h
=> 4×r = 28
=> r = 7 cm.
Diameter = 2 × Radius
=> Diameter = 2 × 7 = 14 cm.
So, the diameter of cone will be 14cm. ✔✔
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Hope it helps ☺
Fóllòw Më ❤
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