question_answer

A solid wooden toy is in the form of a 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 wood used in toy.

A)  \[343.72\text{ }c{{m}^{3}}\]              

B)  \[266.11\text{ }c{{m}^{3}}\]    

C)  \[532.22\text{ }c{{m}^{3}}\]              

D)  \[133.55\text{ }c{{m}^{3}}\]

Correct Answer: B

Solution :

(b): Height of cone \[=10.2-4.2=6\,\,cm\] Volume of wood \[=\frac{\pi {{r}^{2}}h}{3}+\frac{4\pi {{r}^{3}}}{3\times 2}\] \[\Rightarrow \]   \[\frac{3.14\times {{(4.2)}^{2}}\times 6}{3}+\frac{4\times 3.14\times {{(4.2)}^{3}}}{3\times 2}\] \[\Rightarrow \]   \[266.11\,\,c{{m}^{3}}\]