A solid wooden cylinder has radius 5 cm and height 12 cm. A cone of the same radius and height is carved out from one end. Find the volume and total surface area of the remaining solid. (Take π = 3.14.)

1. 1 · Write what is given and what is to be found Cylinder and cone: r = 5 cm, h = 12 cm. To find: the volume and TSA of the solid that is left.
2. 2 · Draw the figure Draw the cylinder. From the circle at the top, draw dotted lines to the centre of the bottom to show the hollow cone. Mark r = 5 cm, h = 12 cm and the slant height l.
3. 3 · Write the formulas Volume left = πr²h − (1/3)πr²h; TSA = 2πrh + πr² + πrl, where l = √(h² + r²).
4. 4 · Find the volume left
   • V = 3.14 × 25 × 12 − 1/3 × 3.14 × 25 × 12
   • = 942 − 314 = 628 cm³
5. 5 · Find the slant height
   • l = √(12² + 5²) = √169 = 13 cm
6. 6 · Find the total surface area
   • Outer curved surface 2πrh = 2 × 3.14 × 5 × 12 = 376.8 cm²
   • Bottom circle πr² = 3.14 × 25 = 78.5 cm²
   • Inner cone surface πrl = 3.14 × 5 × 13 = 204.1 cm²
   • TSA = 376.8 + 78.5 + 204.1 = 659.4 cm²
7. 7 · Check and box the answer Volume = 628 cm³, TSA = 659.4 cm². The top circle is gone, but the inner surface of the hollow is added.

Scoring tip: When a part is carved out, subtract its volume but add its inner surface. Many students subtract the surface as well.