The surface area of a solid metallic sphere is 616 cm². It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use π = 22/7).

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Solution

The surface area of the metallic sphere is 616 square cm. Let the radius of the metallic sphere is r. Therefore, we have

Therefore, the radius of the metallic sphere is 7 cm and the volume of the sphere is

The sphere is melted to recast a cone of height 28 cm. Let the radius of the cone is R cm. Therefore, the volume of the cone is

Since, the volumes of the sphere and the cone are same; we have

Hence, the diameter of the base of the cone so formed is two times its radius, which is cm.

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The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use π = 22/7).

The surface area of a solid metallic sphere is 616 cm². It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use π = 22/7).