# Designing a Rug With Ellipses and Circles

• Jul 5th 2009, 11:28 PM
Designing a Rug With Ellipses and Circles
Louise uses an ellipse (see attachment) and two circles to design a rug. The diagram shows her design, drawn on a number plane.

a. Calculate the area of the shaded region.

How would I do so?

Note: The width of the ellipse is 5 and the radius of the small circle is 3.
• Jul 6th 2009, 12:15 AM
arze
Quote:

Louise uses an ellipse (see attachment) and two circles to design a rug. The diagram shows her design, drawn on a number plane.

a. Calculate the area of the shaded region.

How would I do so?

Note: The width of the ellipse is 5 and the radius of the small circle is 3.

the width of the ellipse is 5 the radius is also 5.
area of ellipse = pi*a*b = pi*5*3
now we only have to deal with one half of the ellipse and larger circle.
so 0.5*pi*5*3
the area of the semicircle would be 0.5*pi*5^2
now area of semicircle minus area of half the ellipse and you get the area of the shaded region
• Jul 6th 2009, 12:36 AM
Thank you for your above post. A good explanation makes Mathematics seem so much easier.

b. Louise is binding the circumference of the smaller circle with wool. She uses 80 g of wool for every metre. How many grams of wool will she use?

Correct me if I am wrong.

2*pi*3 = 18.85 m
18.85*80 = 1508 g

Therefore, she will use 1508 g of wool.
• Jul 6th 2009, 12:39 AM
arze
Quote: