Given a circle, a circumscribed square is one that completely encloses the circle, and an inscribed square is one that is completely enclosed by the circle, as shown below:
If the the difference in the areas of the two squares is 35 sq. m., then what is the area of the circle? (Assume π =
22 |
7 |
Answer:
55 sq. m.
- Let's name the outer square as ABCD, and the inner square as PQRS as shown below:
- If the radius of the circle is R, the side of the outer square will be double of circle's radius:
AB = 2R - Area of outer square,
Area(ABCD) = 2R × 2R = 4R2 - Side of the inner square PQRS can be calculated using Pythagoras Theorem:
PQ = ^@ \sqrt {R^2 + R^2} ^@
or, PQ = √2R - Area of inner square,
Area(PQRS) = √2R × √2R = 2R2 - The difference in areas of the two squares is given to be 35 sq. m.
Thus, Area(ABCD) - Area(PQRS) = 35
⇒ 4R2 - 2R2 = 35
⇒ 2R2 = 35
⇒ R2 =35 2 - Now that we know the radius of the circle, we can calculate the area of the circle using the formula,
Area(circle) = πR2
=
×22 7 35 2
= 55 sq. m.