The difference of the area of the circumscribed and
the inscribed square of a circle is 35 sq. cm. Find the
area of the circle.
Answers
Question :- The difference of the area of the circumscribed and the inscribed square of a circle is 35 sq. cm. Find the area of the circle. ?
Solution :-
Let us assume that, the radius of the circle is r cm.
we know that,
- Side of circumscribed square ABCD = Diameter of circle .
- Diagonal of inscribed square EFGH = Diameter of circle.
- Diagonal of square = √2 * side .
- Area of square = (side)²
- Area of circle = π * (radius)²
given that,
→ Area of circumscribed square ABCD - Area of inscribed square EFGH = 35 cm²
→ (2r)² - (2r/√2)² = 35
→ 4r² - (4r²/2) = 35
→ 4r² - 2r² = 35
→ 2r² = 35
→ r² = (35/2)
therefore,
→ Area of circle = πr²
→ Area of circle = (22/7) * (35/2)
→ Area of circle = 55 cm². (Ans.)
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Answer:
The difference of the area of the circumscribed and the inscribed squares of a circle is 35 sq.cm.... = 22 35 7 2 × = 55 sq.cm.
Step-by-step explanation:
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