Given: The radius and height of a right circular cone are in the ratio 3:7 The volume of the cone is 528cm3 Concept used: Volume of a right circular cone =(1∕3)πr2h r= radius, h= height Calculation: Let the radius and height of the cone be 3y and 7y Now, volume of the cone =(1∕3)π(3y)2×7y According to the question,
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3
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×(3y)2×7y=528 ⇒
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7
×9y2×7y=528 ⇒66y3=528cm3 ⇒6y3=48cm3 ⇒y3=8cm3 ⇒y=2cm So, the height of the cone =7y=7×2=14 ∴ The height of the cone is 14cm.