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A solid sphere has a radius 21 cm. It is melted to form a cube. 20% material is wasted in this process. The cube is melted to form hemisphere. In this process 20% material is wasted. The hemisphere is melted to form two spheres of equal radius. 20% material was also wasted in this process. What is the radius (in cm) of each new sphere?

A solid sphere has a radius 21 cm. It is melted to form a cube. 20% material is wasted in this process. The cube is melted to form hemisphere. In this process 20% material is wasted. The hemisphere is melted to form two spheres of equal radius. 20% material was also wasted in this process. What is the radius (in cm) of each new sphere? Correct Answer <span class="math-tex">\(8.4\left( {\sqrt[3]{4}} \right)\)</span>

According to question,

4/3 × π × 213 × (1 – 20/100) × (1 – 20/100) × (1 – 20/100) = 2 × 4/3 × πr3

Where, r = radius of two new spheres formed,

⇒ 213 × (1 – 20/100) × (1 – 20/100) × (1 – 20/100) = 2 × r3

⇒ 213 × (4/5) × (4/5) × (4/5) = 2 × r3

⇒ 213 × 4/5 × 4/5 × 2/5 = r3

⇒ r3 = 3 × 4

⇒ r = (42/5)∛4

⇒ r = 8.4∛4 cm

∴ Radius of each new sphere = 8.4∛4 cm

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