(a) A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 100 cm, calculate the radius of the circle. [Take (pi = frac{22}{7})].
(b) A rope 60cm long is made to form a rectangle. If the length is 4 times its breadth, calculate, correct to one decimal place, the :
(i) length ; (ii) diagonal of the rectangle.
Explanation
(a) Perimeter of a circle = (2pi r).
Length of a side of square = 2r in terms of r.
Sum of perimeter of circle and square = ((2 pi r) + (4 times 2r))
(2r (pi + 4) = 100)
(r ( frac{22}{7} + 4 ) = 50)
(r = 50 div frac{50}{7})
(r = 7 cm)
(b) (i) L = (4 times breadth)
B = breadth.
60 cm = 2(4B + B)
2(5B) = 60 cm
(B = frac{60}{10} = 6 cm)
(L = 4 times 6 = 24 cm).
(ii)
Let the diagonal be d.
(d^{2} = 6^{2} + 24^{2})
(d^{2} = 36 + 576)
(d^{2} = 612)
(d = sqrt{612})
= (24.74 cm approxeq 24.7 cm).