Math Problem Statement

Find the area of the circle shown below:

412.91 cm2

963.82 cm2

17.5 cm2

26.28 cm2

Find the area of the circle shown below: 412.91 cm2, 963.82 cm2, 17.5 cm2, 26.28 cm2.

Solution

The image you uploaded shows a transformation of a yellow circle into a yellow rectangle with a width labeled as 55 cm. Let's proceed step by step to solve this problem.

From the given options, the area of the circle is asked, and we are provided with a few values:

  • 412.91 cm²
  • 963.82 cm²
  • 17.5 cm²
  • 26.28 cm²

The area of a circle is calculated using the formula:

A=πr2A = \pi r^2

Where:

  • AA is the area of the circle.
  • rr is the radius of the circle.
  • π\pi is a constant approximately equal to 3.1416.

Now, to find the correct area from the options, we need to extract the radius information, which is not provided directly in the image. Let me deduce some information or assume details that could help.

Since the circle transforms into a rectangle with a width of 55 cm, I will assume the circle’s diameter equals the width of the rectangle, which gives a diameter of 55 cm.

Thus, the radius rr would be:

r=552=27.5 cmr = \frac{55}{2} = 27.5 \text{ cm}

Now, let's calculate the area using this radius:

A=π×(27.5)2A = \pi \times (27.5)^2

I will compute this to find the correct area and match it to one of the provided options.The calculated area of the circle is approximately 2375.83 cm². However, none of the provided answer options match this value directly.

Since the problem involves the transformation of the circle into a rectangle, there could be more information needed to fully interpret the correct context, or the options could represent other types of values.

Do you need further clarification, or should we explore additional details about the transformation process?

5 Related Questions:

  1. How is the circumference of a circle related to its radius?
  2. What is the formula for the area of a rectangle, and how does it compare to a circle's area?
  3. How would changing the radius of the circle affect its area?
  4. Can you derive the area of the circle using its circumference instead?
  5. How does a circle’s diameter relate to its area calculation?

Tip:

Always remember that the area of a circle grows quadratically with the radius, meaning doubling the radius will quadruple the area.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle
Area

Formulas

Area of a circle: A = πr²

Theorems

Pythagorean Theorem (implicit in calculations involving radius and diameter)

Suitable Grade Level

Grades 6-8