Calculate Circle Area When Rectangle Area = 28X: Geometric Relationship Problem

The area of the rectangle in the drawing is 28X cm².

What is the area of the circle?

S=28XS=28XS=28X777

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Express the circumference of the circle using X
00:03 The short side is a diameter according to the given data
00:07 Apply the formula to calculate the area of the rectangle: side(7) multiplied by side(2R)
00:10 Insert the relevant values into the formula and solve for R
00:19 Isolate R
00:25 This is the expression for radius(R) using X
00:29 Apply the formula to calculate the circle's circumference
00:36 Substitute the relevant values into the formula and solve to determine the circumference expression
00:45 This is the solution

Step-by-step written solution

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1

Understand the problem

The area of the rectangle in the drawing is 28X cm².

What is the area of the circle?

S=28XS=28XS=28X777

2

Step-by-step solution

Let's draw the center of the circle and we can divide the diameter of the circle into two equal radii

Now let's calculate the length of the radii as follows:

7×2r=28x 7\times2r=28x

14r=28x 14r=28x

We'll divide both sides by 14:

r=2814x r=\frac{28}{14}x

r=2x r=2x

Let's calculate the circumference of the circle:

P=2π×r=2π×2x=4πx P=2\pi\times r=2\pi\times2x=4\pi x

3

Final Answer

4πx 4\pi x

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?
666444AAABBBCCCDDD

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