A spherical cannon ball, 28 cm in diameter, is melted and cast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone.

Asked by Topperlearning User | 27th Oct, 2017, 02:05: PM

Expert Answer:

 

begin mathsize 12px style Volume space of space straight a space sphere space equals space 4 over 3 πr cubed
Diameter space equals space 28 space cm comma space raidus space equals space 14 space cm
Volume space of space straight a space sphere space equals space 4 over 3 straight pi cross times 14 cubed space cm cubed
Volume space of space straight a space cone space equals space 1 third πr squared straight h
Here comma space diameter space equals space 35 space cm space rightwards double arrow radius space equals space 35 over 2 space cm space and space height space equals space straight h space cm
Volume space of space straight a space cone space equals space 1 third straight pi open parentheses 35 over 2 close parentheses squared straight h space cm cubed
Volume space of space straight a space sphere space equals space Volume space of space straight a space cone
4 over 3 straight pi cross times 14 cubed space equals space 1 third straight pi open parentheses 35 over 2 close parentheses squared straight h
straight h space equals space fraction numerator 4 cross times 14 cross times 14 cross times 14 cross times 2 cross times 2 over denominator 35 cross times 35 end fraction
straight h space equals space 896 over 25 space cm
straight h space equals space 35.84 space cm
Hence space the space height space of space conical space mould space equals space 35.84 space cm end style

Answered by  | 27th Oct, 2017, 04:05: PM