A hollow cylindrical iron pipe is 21 cm long. Its outer and inner diameters are 8 cm and 6 cm. Find the volume of iron in it and its total surface area. (Take π = 22/7.)
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Write what is given and what is to be found h = 21 cm, R = 8 ÷ 2 = 4 cm, r = 6 ÷ 2 = 3 cm. To find: volume of iron and TSA.
2 · Draw the figure Draw a hollow cylinder: two circles with the same centre at the top, and dotted lines for the inner hole. Mark R = 4 cm, r = 3 cm and h = 21 cm.
3 · Write the formulas Volume of iron = πh(R² − r²); TSA = 2π(R + r)(R − r + h).
4 · Work out the volume
Volume = 22/7 × 21 × (4² − 3²)
= 22/7 × 21 × (16 − 9)
= 66 × 7 = 462 cm³
5 · Work out the total surface area
TSA = 2 × 22/7 × (4 + 3) × (4 − 3 + 21)
= 2 × 22/7 × 7 × 22
= 44 × 22 = 968 cm²
6 · Check and box the answer The pipe uses 462 cm³ of iron, and its total surface area is 968 cm². Box both, with units.
Scoring tip: Halve the diameters before anything else. Using the diameter as the radius is the most common way to lose the whole sum.
