Discussion
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of toy is 15.5 cm. What is the total surface area of toy in cm2
Answer: C
The total surface area is 214.5 cm².
The hemisphere's height is its radius, 3.5 cm, so the cone's height is \(15.5 - 3.5 = 12\) cm. Its slant height is
\[ \begin{aligned} l &= \sqrt{12^{2} + 3.5^{2}} \\ &= \sqrt{156.25} = 12.5\ \text{cm} \end{aligned} \]
The exposed surface is the cone's curved surface plus the hemisphere's curved surface (the joined circular faces are hidden):
\[ \begin{aligned} \pi r l + 2\pi r^{2} &= \tfrac{22}{7}(3.5)(12.5) + 2 \cdot \tfrac{22}{7}(3.5)^{2} \\ &= 137.5 + 77 = 214.5 \end{aligned} \]
Only the two curved surfaces count; the circular faces where the cone and hemisphere join are hidden inside the toy, and the cone's height is the total height less the hemisphere's radius, not the full 15.5 cm.
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