(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.

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(a) A circle is inscribed in a square. If the sum of the perimeter of the square and ...

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(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

π = \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 =

2 π r

.
Length of a side of square = 2r in terms of r.
Sum of perimeter of circle and square =

(2 π r) + (4 \times 2 r)

2 r (π + 4) = 100

r (\frac{22}{7} + 4) = 50

r = 50 \div \frac{50}{7}

r = 7 c m

(b) (i) L =

4 \times b r e a d t h

B = breadth.
60 cm = 2(4B + B)
2(5B) = 60 cm

B = \frac{60}{10} = 6 c m

L = 4 \times 6 = 24 c m

.
(ii)
Let the diagonal be d.

d^{2} = 6^{2} + 24^{2}

d^{2} = 36 + 576

d^{2} = 612

d = \sqrt{612}

24.74 c m ≊ 24.7 c m

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