MP Board · Class 10 · Mathematics · Surface Areas and VolumesA wooden toy is in the form of a cone mounted on a hemisphere. The diameter of the base of the cone is $6\text{ cm}$ and its height is $4\text{ cm}$. Find the total surface area of the toy. (Use $\pi = 3.14$)

Given data:

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