Math Problem Statement

اوجد محيط الدائرة

اوجد محيط الدائرة

Solution

To find the circumference of the circle from the provided image, we need to extract the following details:

Given Information:

  • The width of the rectangle at the top is 10 meters.
  • The height of the rectangle on the side is 7 meters.
  • The shape beneath the rectangle is a semicircle.

Steps to Find the Circumference of the Circle:

  1. Identify the diameter of the circle: The diameter of the semicircle matches the width of the rectangle, which is 10 meters.

    Diameter (D)=10m\text{Diameter (D)} = 10 \, \text{m}

  2. Calculate the radius of the circle: The radius is half the diameter.

    Radius (r)=D2=102=5m\text{Radius (r)} = \frac{D}{2} = \frac{10}{2} = 5 \, \text{m}

  3. Calculate the circumference of the full circle: The formula for the circumference of a full circle is:

    C=2πr=2π×5=10πmC = 2 \pi r = 2 \pi \times 5 = 10 \pi \, \text{m}

    Therefore, the total circumference of the full circle is 10π10 \pi meters, which is approximately 31.42m31.42 \, \text{m}.

  4. Interpret the question: Since the shape shown in the image is a semicircle, the circumference needed is half of the full circle. Additionally, we include the straight horizontal edge (the diameter) as part of the total perimeter around the shape.

    • The semicircular part's circumference is: Semicircle circumference=C2=10π2=5πm15.71m\text{Semicircle circumference} = \frac{C}{2} = \frac{10 \pi}{2} = 5 \pi \, \text{m} \approx 15.71 \, \text{m}

    • Adding the diameter to the total perimeter: Total perimeter=5π+1015.71+10=25.71m\text{Total perimeter} = 5 \pi + 10 \approx 15.71 + 10 = 25.71 \, \text{m}

Thus, the total perimeter around the semicircle is approximately 25.71 meters.

Let me know if you'd like more details or have questions! Here are 5 related questions for further practice:

  1. What is the formula for the area of a circle?
  2. How would you calculate the area of a semicircle?
  3. If the radius of the circle were 6 meters, what would the circumference be?
  4. What is the relationship between the diameter and circumference of a circle?
  5. How can you calculate the area of a sector of a circle?

Tip: Always ensure that you include all necessary parts of a shape (like straight edges) when calculating perimeters for composite shapes.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circumference
Semicircles

Formulas

C = 2πr
Semicircle Circumference = πr

Theorems

Perimeter of composite shapes
Circle circumference theorem

Suitable Grade Level

Grades 5-7