Math Problem Statement

You have also been asked to help set up the basketball court. 

What is the circumference of the circle? 

(C = πd)

m

What is the area of the circle? 

(A = πr2)

m2 

(give your answer to 2 decimal places.)

(Use π = 3.14)

What is the circumference of the circle? (C = πd) m What is the area of the circle? (A = πr²) m² (give your answer to 2 decimal places.) (Use π = 3.14)

Solution

To solve this, let's calculate the circumference and area of the circle based on the given formulas.

Given Data:

  • Diameter (dd) = 1.8 m
  • Radius (rr) = d2=1.82=0.9m\frac{d}{2} = \frac{1.8}{2} = 0.9 \, \text{m}
  • Use π=3.14\pi = 3.14

Step 1: Calculate the circumference

The formula is: C=πdC = \pi d Substituting the values: C=3.14×1.8=5.652mC = 3.14 \times 1.8 = 5.652 \, \text{m} To two decimal places: C=5.65mC = 5.65 \, \text{m}


Step 2: Calculate the area

The formula is: A=πr2A = \pi r^2 Substituting the values: A=3.14×(0.9)2=3.14×0.81=2.5434m2A = 3.14 \times (0.9)^2 = 3.14 \times 0.81 = 2.5434 \, \text{m}^2 To two decimal places: A=2.54m2A = 2.54 \, \text{m}^2


Final Answers:

  1. Circumference: 5.65m5.65 \, \text{m}
  2. Area: 2.54m22.54 \, \text{m}^2

Would you like a detailed explanation of these steps or help with a related problem?


Here are 5 questions to deepen your understanding:

  1. What would the circumference be if the diameter were doubled?
  2. How does the radius affect the area of a circle?
  3. If π\pi were approximated as 3.1416, how would the results change?
  4. What is the relationship between the diameter and the radius of a circle?
  5. Can you derive the formula for the area of a circle using calculus?

Tip: Always ensure that units match in your calculations to avoid errors!

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle
Circumference
Area

Formulas

Circumference of a circle: C = πd
Area of a circle: A = πr²

Theorems

Basic properties of circles

Suitable Grade Level

Grades 6-8