Math Problem Statement

A circle has a radius of 7 cm. What is the area of the circle? 

Solution

To find the area of a circle, you use the formula:

Area=πr2\text{Area} = \pi r^2

Where:

  • π\pi is approximately 3.14159.
  • rr is the radius of the circle.

Given that the radius r=7cmr = 7 \, \text{cm}, we can substitute this value into the formula:

Area=π×(7)2=π×49\text{Area} = \pi \times (7)^2 = \pi \times 49

Area3.14159×49153.94cm2\text{Area} \approx 3.14159 \times 49 \approx 153.94 \, \text{cm}^2

So, the area of the circle is approximately 153.94 cm².

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the circumference of the same circle?
  2. If the radius of the circle were doubled, what would the new area be?
  3. How would the area change if the radius were halved?
  4. What is the area of a sector of the circle with a 90° angle?
  5. How does the area of a circle compare to the area of a square with the same perimeter?

Tip: The area of a circle grows quadratically with the radius, meaning small changes in the radius lead to larger changes in area.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Area Calculation

Formulas

Area of a circle = πr²

Theorems

Area theorem of a circle

Suitable Grade Level

Grades 6-8