question_answer

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if the height of conical part is 12 cm.

A)  \[1440\text{ }c{{m}^{2}}\]                 

B)  \[385\text{ }c{{m}^{2}}\]      

C)  \[1580\text{ }c{{m}^{2}}\]                 

D)  \[770\text{ }c{{m}^{2}}\]

Correct Answer: D

Solution :

(d): Radius of cylinder, hemisphere and cone = 5 cm Height of cylinder =13 cm; Height of cone =12 Surface area of toy \[=2\pi rh+\frac{4\pi {{r}^{2}}}{2}+\pi rL\]; \[L=\sqrt{{{h}^{2}}+{{r}^{2}}}=\sqrt{{{12}^{2}}+{{5}^{2}}}=13\] Then, surface area =\[(2\times 3.14\times 5\times 13)+(2\times 3.14\times 25)\]\[+(3.14\times 5\times 13)=770\,\,c{{m}^{2}}\]