A steel bucket open at the top is a frustum of height 12 cm. The radii of its top and bottom are 15 cm and 6 cm. Find the area of steel sheet needed and the volume of water it can hold. (Take π = 22/7.)

1. 1 · Write what is given and what is to be found R = 15 cm (open top), r = 6 cm (closed bottom), h = 12 cm. To find: sheet area and volume.
2. 2 · Draw the figure Draw the frustum with the wide end on top. Mark R = 15 cm, r = 6 cm, h = 12 cm and the slant side l. Show the right triangle with sides 12 cm and R − r = 9 cm.
3. 3 · Write the formulas l = √(h² + (R − r)²); sheet = π(R + r)l + πr²; volume = (1/3)πh(R² + Rr + r²).
4. 4 · Find the slant height
   • l = √(12² + 9²) = √(144 + 81)
   • = √225 = 15 cm
5. 5 · Find the sheet area
   • Sheet = 22/7 × (15 + 6) × 15 + 22/7 × 6 × 6
   • = 990 + 113.14 = 1103.14 cm²
6. 6 · Find the volume
   • V = 1/3 × 22/7 × 12 × (225 + 90 + 36)
   • = 1/3 × 22/7 × 12 × 351 = 30888/7
   • ≈ 4412.57 cm³ ≈ 4.41 litres
7. 7 · Check and box the answer Sheet ≈ 1103.14 cm²; volume ≈ 4412.57 cm³, about 4.41 litres. The top is open, so πR² is not added.

Scoring tip: Read which ends are closed. An open bucket adds only the bottom circle; a closed frustum adds both circles.