find area of the largest circle that can be drawn inside the given rectangle of length a centimetre and b centimetre
Answers
solution:-
we know that
Area of circle = πr²
and
in a rectangle length is great than it's breadth [ l > b]
and
we can only draw a circle inside a rectangle with circle's diameter equal to breadth.
=> d = breadth of rectangle = b
=> 2r = b
=> r = b/2
And
the Area of circle with radius (b/2) is
= πr² = π×(b/2)²
=> b²π/ 4 sq. unit.
⭐ hope it helps ⭐
Concept:
A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = πr², (Pi r-squared), where r is the circle's radius. The square unit, such as m², cm², etc., is the unit of area.
Circle area = πr² or πd²/4, in square units.
which equals 22/7 or 3.14
The area a rectangle occupies is the space it takes up inside the limitations of its four sides.
The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter. The area of a square will, however, be equal to the square of side-length in the case of a square because all of its sides are equal.
Perimeter = 2(length +breadth) = 2(l+b)
Area of rectangle = Length x Breadth = lb
Given:
Rectangle of length a centimetre and b centimetre
Find:
Find area of the largest circle that can be drawn inside the given rectangle of length a centimetre and b centimetre
Solution:
we know that
Area of circle = πr²
and
in a rectangle length is great than it's breadth [ l > b]
and
we can only draw a circle inside a rectangle with circle's diameter equal to breadth.
=> d = breadth of rectangle = b
=> 2r = b
=> r= b/2
And the Area of circle with radius (b/2) is = πr² = π×(b/2)²
= b²π/ 4 sq. unit.
Therefore, the area of the largest circl that can be drawn inside the rectangle is b²π/4
#SPJ3