Question: surface area of a sphere = 4\pi r^{2}\nwhere r is the radius.\n\nThe gas tank below is in the shape of a cylinder with an identical hemisphere on each end.\n\nCalculate the surface area of the gas tank.\nGive your answer to 1 d.p.\n\n35 cm\n77 cm\n\nGraph/shape: a horizontal capsule-shaped gas tank is shown in the bottom-center of the page; it consists of a central cylinder with a hemisphere on each end, with a top dimension line labeled 35 cm across the cylinder section and a bottom dimension line labeled 77 cm across the full length, position_hint = bottom-center.
1. **State the problem:** We need to find the surface area of a gas tank shaped as a cylinder with a hemisphere on each end. The cylinder diameter is $35$ cm, and the total length including hemispheres is $77$ cm.\n\n2. **Identify given values:**\n- Radius of cylinder and hemispheres: $r = \frac{35}{2} = 17.5$ cm\n- Total length of tank: $77$ cm\n- Length of cylinder part: $L = 77 - 2r = 77 - 2 \times 17.5 = 77 - 35 = 42$ cm\n\n3. **Formulas to use:**\n- Surface area of a sphere: $$4\pi r^{2}$$\n- Surface area of a hemisphere: $$2\pi r^{2}$$ (half of a sphere)\n- Surface area of a cylinder (side only): $$2\pi r h$$ where $h$ is the height (or length) of the cylinder\n\n4. **Calculate surface area of hemispheres:**\nSince there are two hemispheres, their combined surface area equals the surface area of one full sphere:\n$$2 \times 2\pi r^{2} = 4\pi r^{2}$$\n\n5. **Calculate surface area of cylinder side:**\n$$2\pi r L = 2\pi \times 17.5 \times 42$$\n\n6. **Calculate each part:**\n- Sphere surface area: $$4\pi (17.5)^{2} = 4\pi \times 306.25 = 1225\pi$$\n- Cylinder surface area: $$2\pi \times 17.5 \times 42 = 1470\pi$$\n\n7. **Total surface area:**\n$$1225\pi + 1470\pi = 2695\pi$$\n\n8. **Calculate numerical value:**\n$$2695 \times 3.1416 \approx 8465.1 \text{ cm}^{2}$$\n\n9. **Final answer rounded to 1 decimal place:**\n$$\boxed{8465.1 \text{ cm}^{2}}$$