Adam uses π = 3 to estimate the area of the base of the cone. Work out his estimate.
How to approach this question
First, identify the shape of the base of the cone. It's a circle. Write down the formula for the area of a circle. Identify the radius from the diagram. Substitute the given values for π and the radius into the formula and calculate the result.
Full Answer
The base of the cone is a circle.
The formula for the area of a circle is A = πr².
From the diagram, the radius r = 5 cm.
Adam uses π = 3.
Estimate = 3 × 5²
= 3 × 25
= 75 cm²
The base of a cone is a circle. The formula for the area of a circle is A = πr².
The diagram shows the radius of the base is r = 5 cm.
Adam is using the approximation π = 3.
Substituting these values into the formula:
Area ≈ 3 × (5)²
Area ≈ 3 × 25
Area ≈ 75
So, Adam's estimate for the area of the base is 75 cm².
Common mistakes
✗ Using the formula for circumference (2πr) instead of area (πr²).
✗ Forgetting to square the radius (e.g., 3 × 5 = 15).
✗ Using the height or slant height instead of the radius.
Expert