Math Problem Statement

The diameter of a circle is 94 cm. By first calculating the radius, work out the area of the circle. Give your answer in cm² to 1 decimal place.

Solution

To solve this problem, we follow these steps:

  1. Find the radius: The radius rr of a circle is half of the diameter. Since the diameter is 94 cm, the radius is:

r=942=47cmr = \frac{94}{2} = 47 \, \text{cm}

  1. Calculate the area: The area AA of a circle is given by the formula:

A=πr2A = \pi r^2

Substituting r=47cmr = 47 \, \text{cm}:

A=π×(47)2=π×2209A = \pi \times (47)^2 = \pi \times 2209

A3.1416×22096940.4cm2A \approx 3.1416 \times 2209 \approx 6940.4 \, \text{cm}^2

Thus, the area of the circle is approximately 6940.4 cm² to 1 decimal place.

Would you like more details or have any questions? Here are some follow-up questions:

  1. How would the area change if the diameter were doubled?
  2. Can you explain how the formula for the area of a circle is derived?
  3. What would be the area if the radius were 10 cm smaller?
  4. How would you find the circumference of the same circle?
  5. If the circle represented a real-life object, what could its use be?

Tip: When solving geometry problems, always check units carefully to ensure consistent results.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles

Formulas

Area of a circle: A = πr²
Radius: r = diameter / 2

Theorems

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Suitable Grade Level

Grades 6-8