• Quick retrieval from earlier learning (Find the volume of composite solids; Use length, area and volume scale factors). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. A rocket model is a cylinder (radius 6 cm, height 10 cm) with a cone (same radius, height 5 cm) on top. Find its volume to 1 decimal place. → 1319.5Prompt: Find each part's volume and add them.
2. Two similar shapes have lengths in the ratio 1 : 5. The smaller has area 8 cm². What is the area of the larger? → 200Prompt: Areas scale by the square of the length factor.
3. A capsule is a cylinder of radius 3 cm and length 14 cm with a hemisphere on one end. Find its volume to 1 decimal place. → 452.4Prompt: A hemisphere is half a sphere: ⅔πr³.

• Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
• Share the objective: Find the volume of a frustum. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: A cone has base radius 18 cm and height 12 cm. The top is cut off parallel to the base, leaving a small cone of radius 12 cm and height 8 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
• Step 1: ⅓π(18² × 12 − 12² × 8)
• Step 2: ≈ 2865.1 cm³
• Answer: 2865.1
• Pause after each step and ask a student to say what comes next.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. A cone has base radius 6 cm and height 18 cm. The top is cut off parallel to the base, leaving a small cone of radius 3 cm and height 9 cm removed. Find the volume of the frustum that is left, to 1 decimal place. → 593.8Prompt: Frustum = big cone − small cone.
2. A cone of volume 405π cm³ has its top cut off. The removed cone is similar with a length scale factor of 2/3. What fraction of the original volume is left? Give a fraction. → 19/27Prompt: Volumes scale by the cube of the length factor.

• Students work on the student sheet. Circulate and check the first two answers of every student early.
• Students who finish: write a question of their own for a partner, with the answer.

The 6 questions are on the student sheet below, with answers in the key.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. A cone has base radius 18 cm and height 18 cm. The top is cut off parallel to the base, leaving a small cone of radius 12 cm and height 12 cm removed. Find the volume of the frustum that is left, to 1 decimal place. → 4297.7Prompt: Frustum = big cone − small cone.
2. A cone of volume 144π cm³ has its top cut off. The removed cone is similar with a length scale factor of 1/3. What fraction of the original volume is left? Give a fraction. → 26/27Prompt: Volumes scale by the cube of the length factor.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-10.