a cone of the height 24cm and radius of base 6cm is made up of modelling clay. a child reshapes it in the form of a sphere. find the radius of the sphere.
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The radius of the sphere is 6cm.
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Height of the cone = 24cm
base radius of the cone = 6cm
it's volume = 1/3πr²h
= 1/3 × 22/7 × 6 × 6 × 24
= 22/7 × 2 × 6 × 24
= 6336/7cm³
according to the question, the cone us remoulded in the form of a sphere.
therefore volume of the cone = volume of the sphere
→ 4/3πr³ = 6336/7cm³
→ 4/3 × 22/7 × r³ = 6336/7cm³
→ 88/21 × r³ = 6336/7cm³
→ r³ = 6336/7 × 21/88
→ r³ = 72 × 3
→ r³ = 216
→ r = ³√216
→ r = 6cm
hence, the radius of the sphere is 6cm.
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