The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm and breadth 7 cm. What is the circumference of a semi-circle whose diameter is equal to the side of the square ? (rounded off to two decimal places)
A. 23.57 cm
B. 38.57 cm
C. 42.46 cm
D. 47.47 cm
E. None of these
Answer: Option A
Solution(By Examveda Team)
Perimeter of rectangle :$$\eqalign{ & = \left[ {2\left( {8 + 7} \right)cm} \right] \cr & = 30\,cm \cr} $$
Perimeter of square :
$$\eqalign{ & = \left( {2 \times 30} \right)cm \cr & = 60\,cm \cr} $$
Side of the square :
$$\eqalign{ & = \left( {\frac{{60}}{4}} \right)cm \cr & = 15\,cm \cr} $$
Radius of the semi-circle $$ = \left( {\frac{{15}}{2}} \right)cm$$
∴ Circumference :
$$\eqalign{ & = \left( {\frac{{22}}{7} \times \frac{{15}}{2}} \right)cm \cr & = \left( {\frac{{165}}{7}} \right)cm \cr & = 23.57\,cm \cr} $$
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what is the formula of Circumference of semi circle ?, i suppose ,you have forgotten to add 2r.