The radii of the bases of three right circular metallic cones of same height ‘h’ are 8 cm, 16 cm and 24 cm. The
cones are melted together and recast into a solid sphere of radius 28 cm. Find the value of ‘h’.
Answers
Given : The radii of the bases of three right circular metallic cones of same height ‘h’ are 8 cm, 16 cm and 24 cm.
The cones are melted together and recast into a solid sphere of radius 28 cm.
To Find : the value of ‘h’.
Solution:
Volume of cone = (1/3)πr²h
Volume of 8 cm radius cone = (1/3)π8²h
Volume of 16 cm radius cone = (1/3)π16²h
Volume of 24 cm radius cone = (1/3)π24²h
Total Volume = (1/3)π8²h + (1/3)π16²h + (1/3)π24²h
= (1/3)π8²h(1 + 2² + 3²)
= (1/3)π8²h(1 + 4 + 9)
= (1/3)π8²h(14)
Volume of sphere = (4/3)πr³
Volume of 28 cm radius sphere = (4/3)π28³
Equate volume
(1/3)π8²h(14) = (4/3)π28³
=> h = 4 * 28³ / 8² * 14
=> h = 4 * 28 * 28 *2 / 8 * 8
=> h = 28 * 28 / 8
=> h = 7 * 14
=> h = 98 cm
Value of h = 98 cm
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