1. **State the problem:** We need to find the surface area of a cylindrical display stand with radius $AB = 7.8$ cm and height $BC = 21.1$ cm. 2. **Identify the formulas:** - Radius $r = AB = 7.8$ cm - Height $h = BC = 21.1$ cm - Area of base (circle) $= \pi r^2$ - Circumference of base $= 2 \pi r$ - Lateral surface area $= \text{circumference} \times h = 2 \pi r h$ - Total surface area $= 2 \times \text{area of base} + \text{lateral surface area}$ 3. **Calculate the area of the base:** $$\text{Area of base} = 3.14 \times (7.8)^2 = 3.14 \times 60.84 = 190.98 \text{ cm}^2$$ 4. **Calculate the circumference of the base:** $$\text{Circumference} = 2 \times 3.14 \times 7.8 = 6.28 \times 7.8 = 48.98 \text{ cm}$$ 5. **Height of the cylinder:** $$BC = 21.1 \text{ cm}$$ 6. **Calculate the lateral surface area:** $$\text{Lateral surface area} = 48.98 \times 21.1 = 1033.68 \text{ cm}^2$$ 7. **Calculate the total surface area:** $$\text{Surface area} = 2 \times 190.98 + 1033.68 = 381.96 + 1033.68 = 1415.64 \text{ cm}^2$$ **Final answers:** - Radius $AB = 7.8$ cm - Area of base $= 190.98$ square centimeters - Circumference of base $= 48.98$ centimeters - Height $BC = 21.1$ centimeters - Lateral surface area $= 1033.68$ square centimeters - Surface area of the display stand $= 1415.64$ square centimeters