Question: 2. The object shown in Figure 2 is made up from a cylinder and a hemisphere. The cylinder has radius 7 cm and height 21 cm.
How would you explain to your students the surface area of the object? Illustrate in detail.
(Surface area of a sphere = 4\pi r^2 , \pi = 22/7 )
Figure shows a composite solid made of a cylinder with a hemisphere on top, labeled radius 7 cm and height 21 cm, position_hint = center.
Figure 1/ Rajah 1
( Total / Jumlah: 20 )
1. **State the problem:** We need to find the total surface area of a composite solid made of a cylinder with a hemisphere on top. The cylinder has radius $7$ cm and height $21$ cm.
2. **Recall formulas:**
- Surface area of a cylinder (without top and bottom) is $2\pi rh$ where $r$ is radius and $h$ is height.
- Surface area of a sphere is $4\pi r^2$.
- Surface area of a hemisphere (half a sphere) is half the sphere's surface area plus the base circle area: $2\pi r^2 + \pi r^2 = 3\pi r^2$.
3. **Important note:** Since the hemisphere is on top of the cylinder, the base of the hemisphere coincides with the top circle of the cylinder, so that circle is not exposed and should not be counted twice.
4. **Calculate the curved surface area of the cylinder:**
$$
2\pi rh = 2 \times \frac{22}{7} \times 7 \times 21
$$
Simplify:
$$
2 \times \frac{22}{7} \times 7 \times 21 = 2 \times 22 \times 21 = 924
$$
5. **Calculate the surface area of the hemisphere (curved part only):**
$$
2\pi r^2 = 2 \times \frac{22}{7} \times 7^2 = 2 \times \frac{22}{7} \times 49
$$
Simplify:
$$
2 \times 22 \times 7 = 308
$$
6. **Add the two surface areas to get total surface area:**
$$
924 + 308 = 1232 \text{ cm}^2
$$
7. **Final answer:** The total surface area of the composite solid is $1232$ cm$^2$.
This includes the curved surface of the cylinder and the curved surface of the hemisphere on top, excluding the base circle where they join.