Math Problem Statement

Use the following figure for the next 2 questions: Find the circumference and area of a circle with a radius of 9 cm.

Solution

The image shows a circle with a radius of 9 cm, and you are tasked with finding the circumference and area of the circle. Here's how we can solve both problems:

Question 8: Find the Circumference

The formula for the circumference CC of a circle is:

C=2πrC = 2 \pi r

Where:

  • π3.14\pi \approx 3.14 (as given),
  • r=9r = 9 cm.

Substitute the values:

C=2×3.14×9=56.52cmC = 2 \times 3.14 \times 9 = 56.52 \, \text{cm}

So, the circumference is 56.52 cm.


Question 9: Find the Area

The formula for the area AA of a circle is:

A=πr2A = \pi r^2

Substitute the values:

A=3.14×(9)2=3.14×81=254.34cm2A = 3.14 \times (9)^2 = 3.14 \times 81 = 254.34 \, \text{cm}^2

So, the area is 254.34 cm².


Do you want further details or have any questions?

Here are 5 related questions for practice:

  1. What would the circumference be if the radius were 12 cm?
  2. How does the area of the circle change if the radius is doubled?
  3. What is the formula for the diameter of a circle, and how can it help in finding the circumference?
  4. How would you find the radius if you only knew the circumference?
  5. How can you calculate the area if you are given the diameter instead of the radius?

Tip: Always double-check the units you're working with, especially for area and circumference!

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle Measurements

Formulas

Circumference formula: C = 2πr
Area formula: A = πr^2

Theorems

Geometry of circles

Suitable Grade Level

Grades 6-8