Math Problem Statement

The radius, r, of the circle below is 11 cm. Calculate the area of the circle. Give your answer to 1 d.p.

Solution

To calculate the area of the circle, we will use the formula for the area of a circle:

Area=πr2\text{Area} = \pi r^2

where:

  • r=11cmr = 11 \, \text{cm} (the radius).

Substitute the value of rr into the formula:

Area=π(11)2=π×121\text{Area} = \pi (11)^2 = \pi \times 121

Using the approximation π3.1416\pi \approx 3.1416:

Area=3.1416×121380.132cm2\text{Area} = 3.1416 \times 121 \approx 380.132 \, \text{cm}^2

Rounding to one decimal place:

Area380.1cm2\text{Area} \approx 380.1 \, \text{cm}^2

So, the area of the circle is approximately 380.1cm2380.1 \, \text{cm}^2.

Let me know if you need further details or if you have any questions! Here are some related questions you might find useful:

  1. How does changing the radius affect the area of a circle?
  2. What is the relationship between the radius and circumference of a circle?
  3. How do you calculate the area of a sector of a circle?
  4. What happens to the area of a circle if the radius is doubled?
  5. What is the formula to calculate the circumference of a circle?

Tip: The area of a circle is proportional to the square of its radius, so even a small change in the radius can significantly affect the area.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of a Circle

Formulas

Area = πr²

Theorems

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Suitable Grade Level

Grades 6-8