A wooden toy is in the form of a cone mounted on a hemisphere. The diameter of the base of the cone is $6 ext{ cm}$ and

Question

A wooden toy is in the form of a cone mounted on a hemisphere. The diameter of the base of the cone is $6	ext{ cm}$ and its height is $4	ext{ cm}$. Find the total surface area of the toy. (Use $\pi = 3.14$)

Accepted Answer

Given data: Diameter of the cone's base ($d$) = $6	ext{ cm}$ Radius of the cone and hemisphere ($r$) = $\frac{d}{2} = \frac{6}{2} = 3	ext{ cm}$ Height of the cone ($h$) = $4	ext{ cm}$ Value of $\pi = 3.14$ 
Step 1: Find the slant height ($l$) of the cone.
The formula for slant height is: $$l = \sqrt{r^2 + h^2}$$
Substitute the values of $r$ and $h$: $$l = \sqrt{3^2 + 4^2}$$ $$l = \sqrt{9 + 16}$$ $$l = \sqrt{25} = 5	ext{ cm}$$ 
Step 2: Calculate the curved surface area (CSA) of the cone. $$	ext{CSA of cone} = \pi rl$$ $$	ext{CSA of cone} = 3.14 	imes 3 	imes 5$$ $$	ext{CSA of cone} = 3.14 	imes 15 = 47.1	ext{ cm}^2$$ 
Step 3: Calculate the curved surface area (CSA) of the hemisphere. $$	ext{CSA of hemisphere} = 2\pi r^2$$ $$	ext{CSA of hemisphere} = 2 	imes 3.14 	imes (3)^2$$ $$	ext{CSA of hemisphere} = 2 	imes 3.14 	imes 9$$ $$	ext{CSA of hemisphere} = 18 	imes 3.14 = 56.52	ext{ cm}^2$$ 
Step 4: Calculate the total surface area of the toy. $$	ext{Total Surface Area} = 	ext{CSA of cone} + 	ext{CSA of hemisphere}$$ $$	ext{Total Surface Area} = 47.1 + 56.52 = 103.62	ext{ cm}^2$$ 
Answer:
The total surface area of the toy is $103.62	ext{ cm}^2$.

Surface Areas and Volumes

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