A grain silo is a cylinder of radius 6 m and height 10 m with a hemispherical dome on top. Find (i) the volume of grain it holds when full, (ii) the area of metal sheet for the walls and dome, with no floor. (Use π = 3.14.)

1. 1 · Write what is given and what is to be found. Given r = 6 m, cylinder height h = 10 m; the dome is a hemisphere of radius 6 m. To find: the volume, and the sheet area without the floor.
2. 2 · Draw the figure. Draw a cylinder with a half-circle dome on top. Show the joining circle dotted. Mark r = 6 m and h = 10 m.
3. 3 · Write the formulas.
   • Volume = πr²h + (2/3)πr³.
   • Sheet area = 2πrh + 2πr² (the joining circle is hidden and there is no floor).
4. 4 · Find the volume. V = π × 36 × 10 + (2/3) × π × 216 = 360π + 144π = 504π = 504 × 3.14 = 1582.56 m³.
5. 5 · Find the sheet area. Area = π × 2 × 6 × 10 + π × 2 × 36 = 120π + 72π = 192π = 192 × 3.14 = 602.88 m².
6. 6 · Say what it means. The silo holds 1582.56 m³ of grain and needs 602.88 m² of metal sheet.
7. 7 · Check and box the answer. Volume is in m³ and area in m². Box both answers.

Scoring tip: Take π out as a common factor early, as in 504π. It keeps the numbers small and the working clear.