Problem Statement
A toy is in the form of a cone of radius $3.5\text{ cm}$ mounted on a hemisphere of same radius. The total height of the toy is $15.5\text{ cm}$. Find the total surface area of the toy. (Take $\pi = 22/7$)
Verified Solution & Marking Scheme
Extract Dimensions
Radius $r = 3.5\text{ cm} = \frac{7}{2}\text{ cm}$.
Height of cone $h = 15.5 - 3.5 = 12\text{ cm}$.
Calculate Slant Height l of Cone
$l = \sqrt{r^2 + h^2} = \sqrt{(3.5)^2 + 12^2} = \sqrt{12.25 + 144} = \sqrt{156.25} = 12.5\text{ cm}$
Compute Total Surface Area
$\text{TSA} = \text{CSA of cone} + \text{CSA of hemisphere} = \pi r l + 2\pi r^2 = \pi r (l + 2r)$
$= \frac{22}{7} \times \frac{7}{2} [12.5 + 2(3.5)] = 11 [12.5 + 7] = 11 \times 19.5 = 214.5\text{ cm}^2$