Q. 24.4( 42 Votes )

A toy is made in the form of hemisphere surmounted by a right cone whose circular base is joined with the plane surface of the hemisphere. The radius of the base of the cone is 7 cm. and its volume is of the hemisphere. Calculate the height of the cone and the surface area of the toy correct to 2 places of decimal


Answer :

Given that, The radius of the base(r) of the cone is 7 cm and its volume is of the hemisphere.

circular base of cone is joined with the plane surface of the hemisphere,


radius of hemisphere = radius of base of cone = 7 cm


Also,vol. of cone = vol. of hemisphere



h = 3r


h = 3 × 7


h = 21 cm


Also, slant height(l) = √ r2 + h2


l = √ 72 + 212


l = √ 490


l = 22.13


Slant Height of cone (l) = 22.13 cm


Now, surface area of toy = surface area of cone + surface area of hemisphere


surface area of toy = πrl + 2πr2


= πr(l + 2r)




= 794.86 cm2


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :