Week 26 · Solid shapes and measuring volume with cubes · 3 lessons
3
Estimating volume with unit cubes
Discover Mathematics P5: Term 2, Unit 11, Lessons 1–3
GoalEstimate the volume of a box by thinking in layers and rounding, then compare with the exact volume.
New words
estimate · a close answer made with easy numbersround · to change a number to a nearby easy number, such as 19 to 20fill · to cover the inside of a container completely
Explanation
When you cannot count every cube, estimate. Look at how many cubes fit along the length, the width and the height. Round the numbers to easy ones, then multiply: length × width gives the cubes in one layer, and multiplying by the number of layers gives the volume. For a box 9 cm long, 6 cm wide and 4 cm high, round 9 to 10: 10 × 6 × 4 = 240 cm³. The exact volume is 9 × 6 × 4 = 216 cm³, so the estimate was close. We can also use layers to find a partly filled box: if the box holds 24 cubes in a layer and is filled to 3 layers, it contains 24 × 3 = 72 cubes. Always ask: is my answer sensible? A box of 9 by 6 by 4 cannot hold 5,000 unit cubes.
Worked examples
A box is about 5 cubes long, 4 wide and 3 high. One layer: 5 × 4 = 20 cubes. Three layers: 20 × 3 = 60 cubes. The box holds about 60 unit cubes.
Estimate and then find the exact volume of a box 9 cm by 6 cm by 4 cm. Estimate: 10 × 6 × 4 = 240 cm³. Exact: 9 × 6 = 54, and 54 × 4 = 216 cm³. The estimate is 24 cm³ more than the exact volume.
A box holds 24 cubes in one layer and is 5 layers tall. Its volume when full is 24 × 5 = 120 cubes. Salma has filled it up to 3 layers: 24 × 3 = 72 cubes. She still needs 120 − 72 = 48 cubes.
Class activity
Guess and check. Choose a small box (a tea box or a pencil case). Measure it in centimetres, round each measure, and estimate how many 1 cm cubes would fill it. Then find the exact volume by multiplying. How close was your estimate? Try a second box.
Practice
1
Estimate the volume of a box 11 cm by 5 cm by 3 cm, then find the exact volume.
