Question

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 $13cm$ and $5cm$, respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of toy if the height of the conical part is $12cm.$

• A. $660c{m}^2$
• B. $770c{m}^2$
• C. $880c{m}^2$
• D. $990c{m}^2$

Answer 1

The correct option is B $770c{m}^2$

In $\Delta ABC,AC=\sqrt{{\left(AB\right)}^2+{\left(BC\right)}^2}=\sqrt{{\left(12\right)}^2+{\left(5\right)}^2}AC=\sqrt{169}=13cm$
$\therefore$ Surface area of toy $=\pi rl+2\pi rh+2\pi r^2=\frac{22}{7}\times 5\times 13+2\times \frac{22}{7}\times 5\times 13+2\times \frac{22}{7}\times 5\times 5=\frac{1430}{7}+\frac{2860}{7}+\frac{1100}{7}=\frac{5390}{7}=770{cm}^2$
Hence, the answer is $770c{m}^2$.