A sphare of a diameter 15.6 cm. is melted and cast into a right circular cone of height 31.2 cm. find the diameter of base of the cone
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A sphare of a diameter 15.6 cm. is melted and cast into a right circular cone of height 31.2 cm. find the diameter of base of the cone
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Answer:
Diameter of a sphere = 15.6 cm
Step-by-step explanation:
Radius of the sphere = 15.6 / 2 = 7.8 cm
Volume of a sphere = 4/3 πr3
Volume of the sphere = 4/3 x 22/7 x 7.8 x 7.8 x 7.8
Height of the cone = 31.2 cm
Let the radius of the cone be 'r' cm.
Volume of a cone = 1/3 x πr2h
Volume of the cone = 1/3 x 22/7 x r2 x 31.2
Volume of the cone = Volume of the sphere
1/3 x 22/7 x r2 x 31.2 = 4/3 x 22/7 x 7.8 x 7.8 x 7.8
⇒ r2 = (7.8)2
⇒ r = 7.8 cm
Radius of the cone = 7.8 cm
∴ Diameter of the cone = 2 x 7.8 = 15.6 cm