question_answer

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.

A) \[266.11\text{ }c{{m}^{3}}\]               

B) \[~301.12\,c{{m}^{3}}\]    

C)        \[242.36\text{ }c{{m}^{3}}\]   

D)        \[278.34\,c{{m}^{3}}\]       

Correct Answer: A

Solution :

Let the radius of the hemisphere and base of cone be rand the height of the conical part of the toy be h. Then, r = OA = 4.2 cm, h = VO = VO? - OO? = h = 6 cm Volume of the wooden toy = Volume of the conical part + Volume of the hemi - spherical part