Math Problem Statement

Find the area and circumference of a circle with a diameter of 7 cm. Use 3.14 for π.

Solution

To find the area and circumference of the circle, we'll use the following formulas:

  1. Circumference: C=πdC = \pi \cdot d where d=7d = 7 cm and π=3.14\pi = 3.14.

  2. Area: A=πr2A = \pi \cdot r^2 where r=d2=72=3.5r = \frac{d}{2} = \frac{7}{2} = 3.5 cm.

Step-by-step calculation:

Circumference:

C=3.147=21.98cmC = 3.14 \cdot 7 = 21.98 \, \text{cm}

Area:

A=3.14(3.5)2=3.1412.25=38.465cm2A = 3.14 \cdot (3.5)^2 = 3.14 \cdot 12.25 = 38.465 \, \text{cm}^2

Thus:

  • Area = 38.465 cm²
  • Circumference = 21.98 cm

Let me know if you'd like further details or have any questions!

Here are five related questions:

  1. What is the formula for the area of a sector of a circle?
  2. How would the area change if the diameter was doubled?
  3. Can you find the radius if the circumference is known?
  4. What is the relationship between diameter and radius?
  5. What units should be used for circumference and area?

Tip:

Always make sure to keep track of units in every step of your calculation to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle Properties

Formulas

Circumference of a circle: C = π × d
Area of a circle: A = π × r²

Theorems

Basic Circle Theorems

Suitable Grade Level

Grades 6-8