A toy is shaped by placing a cone on top of a hemisphere. The radius of both the hemisphere and the cone is $36 ext{ cm}$, and the height of the cone is $105 ext{ cm}$. What is the total surface area of the toy in $ ext{cm}^2$?

Question

A toy is shaped by placing a cone on top of a hemisphere. The radius of both the hemisphere and the cone is $36 	ext{ cm}$, and the height of the cone is $105 	ext{ cm}$. What is the total surface area of the toy in $	ext{cm}^2$?

Accepted Answer

**Solution:**

1. Given:
   - Radius of hemisphere and cone, $r = 36 	ext{ cm}$
   - Height of cone, $h = 105 	ext{ cm}$

2. Calculate the slant height $l$ of the cone using Pythagoras theorem:
   $$l = \sqrt{r^2 + h^2} = \sqrt{36^2 + 105^2} = \sqrt{1296 + 11025} = \sqrt{12321} = 111 	ext{ cm}$$

3. Curved surface area of the cone:
   $$= \pi r l = \pi 	imes 36 	imes 111 = 3996\pi 	ext{ cm}^2$$

4. Curved surface area of the hemisphere:
   $$= 2\pi r^2 = 2 \pi 	imes 36^2 = 2 \pi 	imes 1296 = 2592\pi 	ext{ cm}^2$$

5. Total surface area of the toy (excluding the base of the hemisphere which is covered by the cone):
   $$= 3996\pi + 2592\pi = 6588\pi 	ext{ cm}^2$$

**Answer:** $6588\pi 	ext{ cm}^2$

Answer

Answer

Answer