Find the total surface area of a hollow cylinder of internal radius 3 cm thickness 1 cm and height 14 cm
- 330 cm$\displaystyle ^{3}$
- 660 cm$\displaystyle ^{2}$
- 990 cm$\displaystyle ^{2}$
- 1320 cm$\displaystyle ^{2}$
Total surface area of a hollow cylinder = 2 * pi * (R + r) * h + 2 * pi * (R^2 - r^2). R = 3+1 = 4, r = 3, h = 14. Area = 2 * pi * (4+3) * 14 + 2 * pi * (16 - 9) = 2 * pi * 7 * 14 + 2 * pi * 7 = 196 * pi + 14 * pi = 210 * pi. Using pi = 22/7, Area = 210 * 22/7 = 30 * 22 = 660.
To find the total surface area of the hollow cylinder, the outer radius is the internal radius plus the thickness, making it 4 cm. Using the formula for total surface area of a hollow cylinder, 2 times pi times the outer radius plus the inner radius times the sum of the outer radius plus the inner radius plus the height, we get 2 times 22 over 7 times 7 times 15. This simplifies to 44 times 15, giving a total surface area of 660 cm^2.