Math Problem Statement

Find the area of a circle with a radius of 10 cm, using π = 3.14.

Solution

The question you're working on asks to find the area of a circle with a radius of 10 cm, using π=3.14\pi = 3.14. The formula for the area of a circle is:

A=πr2A = \pi r^2

Where:

  • rr is the radius
  • π\pi is approximately 3.14

Given that r=10r = 10 cm, we can substitute this into the formula:

A=3.14×(10)2=3.14×100=314cm2A = 3.14 \times (10)^2 = 3.14 \times 100 = 314 \, \text{cm}^2

Thus, the correct answer is 314 cm².

Do you have any other questions or would you like further details?

Here are 5 related questions to deepen your understanding:

  1. How would the area change if the radius were doubled?
  2. What is the circumference of this circle?
  3. How would using a more precise value of π\pi (e.g., 3.14159) affect the answer?
  4. How do you calculate the area of a sector of a circle?
  5. What is the relationship between the radius and the diameter of a circle?

Tip: Always remember that the area grows proportionally to the square of the radius. So, even a small increase in radius results in a large increase in area!

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Area Calculation

Formulas

Area of a circle: A = πr²

Theorems

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Suitable Grade Level

Grades 6-8