Problem Statement
A solid wooden toy is in the shape of a cone mounted on a hemisphere with a common base of radius $7\text{ cm}$. The total height of the toy is $31\text{ cm}$. Find the total surface area of the toy. (Take $\pi = 22/7$)
Verified Solution & Marking Scheme
Cone Dimensions
Radius $r = 7\text{ cm}$. Height of cone $h = 31 - 7 = 24\text{ cm}$.
Slant height $l = \sqrt{r^2 + h^2} = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25\text{ cm}$.
Calculate Surface Areas
Curved surface area of cone $= \pi r l = \frac{22}{7} \times 7 \times 25 = 550\text{ cm}^2$.
Curved surface area of hemisphere $= 2\pi r^2 = 2 \times \frac{22}{7} \times 49 = 308\text{ cm}^2$.
Total Surface Area
$\text{TSA} = 550 + 308 = 858\text{ cm}^2$