Question

38. A Cone with base radius 10 cm is cut at the centre to take off another Cone. What
is the ratio of volumes of new cone and remaining frustrum of cone.

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Answer 1

Step-by-step explanation:

Given  A Cone with base radius 10 cm is cut at the centre to take off another Cone. What  is the ratio of volumes of new cone and remaining frustum of cone.

• Let the height of the cone be h and base radius be R as the cone is divided into two parts

• Triangle AED is similar to triangle ABC
• By condition of similarity we get
• OE / PC = AO / AP
•              = AO / 2 AO
•              = OE / R
•             = 1/2  
•      OE = R / 2
• We know tvat volume of a cone = 1/3 π r^2 h
• Volume of frustum = volume of cone ABC – volume of cone AED
•       1/3 π R^2 h – 1/3 π (R/2)^2(h/ 2)
•        1/3 π R^2 h(1 – 1/8)  
•        = 1/3 π R^2 h (1/7)
• Now ratio will be 1/8 x 1/3 π R^2 h / 7/8 x 1/3 π R^2 h
•                                 = 1 / 7
•                                  = 1 : 7

Reference link will be

https://brainly.in/question/2027019