ExpertEasy1 markMultiple Choice
AQA GCSE · Question 07.3 · Geometry and Measures
Beth uses π = 3.14 to estimate the area of the base of the cone. Is Beth's estimate more than or less than Adam's estimate? Give a reason for your answer.
Beth uses π = 3.14 to estimate the area of the base of the cone. Is Beth's estimate more than or less than Adam's estimate? Give a reason for your answer.
Answer options:
A.
More than
B.
Less than
How to approach this question
Compare the value of π that Beth uses (3.14) with the value Adam uses (3). The rest of the calculation (multiplying by r²) is the same for both. If you multiply the same number by a larger value, will the result be larger or smaller? Select the correct box and write down this reasoning.
Full Answer
A.More than✓ Correct
Box ticked: More than
Reason: Beth is using a larger value for π (3.14 > 3). Since the radius is the same for both calculations, multiplying by a larger number will result in a larger answer.
Adam's estimate is 3 × r².
Beth's estimate is 3.14 × r².
The value of r² (which is 5² = 25) is the same in both calculations.
We are comparing 3 × 25 with 3.14 × 25.
Since 3.14 is greater than 3, the result of multiplying by 3.14 will be greater than the result of multiplying by 3.
Therefore, Beth's estimate is more than Adam's estimate.
Common mistakes
✗ Ticking the correct box but giving no reason, or an incorrect reason.
✗ Performing the full calculation for Beth's estimate (3.14 x 25 = 78.5) without explicitly stating that 3.14 > 3. While this shows the answer is bigger, the reason should focus on the input values.
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