The Area of a Circle a Is the Sum of Areas of Two Small Circles of Diameter 10Cm and 24 Cm, the Diameter of the Circle a Is?

Let's explore circles together! Think about two small circles, one with a size of 10cm and the other with 24cm. Now, there's a bigger circle called Circle A. The area of Circle A is like putting together the areas of those two small circles. Let's find out its diameter!"

The area of a circle A is the sum of areas of two small circles of diameter 10cm and 24 cm, the diameter of the circle A is?

The diameter of the larger circle A is 26 cm.

Explanation

We can solve this problem by equating the area of circle a to the sum of the areas of the two smaller circles, and then solving the resulting equation for the diameter of circle a.

Steps to solve: 1. Express the areas of the circles in terms of their diameters:

• Area of circle a: πr²
• Area of smaller circle 1: π(10/2​)²=25π
• Area of smaller circle 2: π(24/2​)²=144π

2. Set up the equation: πr² = 25π+144π

3. Solve the equation for r:

• Combine like terms: πr² = 169π
• Divide both sides by π: r² = 169
• Take the square root of both sides: r = ±13

4. Find the diameter: Diameter = 2r = 2⋅13 = 26 cm

Answer: The diameter of circle a is 26 cm.

Area and Perimeter of a Circle

Let's explore the area and perimeter of a circle:

Area of a Circle:

The area of a circle is the amount of space enclosed within its circular boundary. It can be calculated using the following formula:

Area of a circle = πr², where:

• π (pi) is a mathematical constant approximately equal to 3.14159.
• r is the radius of the circle, which is the distance from the center of the circle to any point on its edge.

Perimeter of a Circle:

The perimeter of a circle, also known as its circumference, is the total length of its boundary. It can be calculated using the following formula:

Perimeter of a circle = 2πr, where:
* π (pi) is the same mathematical constant as mentioned above.
* r is the radius of the circle.

Example:

Suppose you have a circle with a radius of 5 centimeters. Let's calculate its area and perimeter:

• Area of the circle = πr² = 3.14159 * 5² ≈ 78.54 square centimeters
• Perimeter of the circle = 2πr = 2 * 3.14159 * 5 ≈ 31.42 centimeters

Key Points:

• The area and perimeter of a circle are directly proportional to the square and the radius of the circle, respectively.
• Understanding these formulas is crucial for various applications in geometry, physics, engineering, and other fields.