Examples with solutions for Circumference: Using variables

Exercise #1

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

What is the area of the circle?

S=28XS=28XS=28X777

Video Solution

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

Answer

4πx 4\pi x

Exercise #2

What is the radius of a circle that has a circumference of 9aπ 9a\pi cm?

Video Solution

Answer

4.5a 4.5a cm

Exercise #3

A circle has a circumference measuring 4xπ 4x\pi cm.

How will the circumference change if we increase the radius of the circle by 2 cm?

Video Solution

Answer

It will increase by 4π 4\pi cm.

Exercise #4

A circle has an area of 81a2π 81a^2\pi .

What is its circumference?

Video Solution

Answer

18aπ 18a\pi cm

Exercise #5

The circumference of the circle in the diagram is 36a2 36a^2 cm.

BO is the radius.

ABCD is a parallelogram.
BO is perpendicular to DC.

DC = 4a \frac{4}{a}

What is the area of the parallelogram?

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Video Solution

Answer

72aπ 72\frac{a}{\pi} cm²