Subjects geometry

Gas Tank Surface Area A20536

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1. **State the problem:** Calculate the surface area of a gas tank composed of a cylinder with two hemispheres on each end. 2. **Given data:** Diameter of cylinder and hemispheres = 45 cm, so radius $r = \frac{45}{2} = 22.5$ cm. 3. **Total length of gas tank:** 79 cm. 4. **Find the length of the cylindrical part:** The gas tank length includes two hemispheres, which together form a full sphere of diameter 45 cm. Length of two hemispheres = diameter = 45 cm. Length of cylinder = total length - length of two hemispheres = $79 - 45 = 34$ cm. 5. **Surface area formulas:** - Surface area of a sphere: $4\pi r^2$ - Surface area of a cylinder (excluding ends): $2\pi r h$ 6. **Calculate surface area of the two hemispheres:** Two hemispheres make one full sphere, so surface area = $4\pi r^2$ 7. **Calculate surface area of the cylindrical part:** $2\pi r h = 2\pi \times 22.5 \times 34$ 8. **Calculate values:** - Sphere surface area = $4\pi (22.5)^2 = 4\pi \times 506.25 = 2025\pi$ - Cylinder surface area = $2\pi \times 22.5 \times 34 = 1530\pi$ 9. **Total surface area:** $$ 2025\pi + 1530\pi = (2025 + 1530)\pi = 3555\pi $$ 10. **Numerical value:** $$ 3555 \times 3.1416 \approx 11166.4 \text{ cm}^2 $$ 11. **Final answer rounded to 1 decimal place:** Surface area $\approx 11166.4$ cm$^2$