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)
Correct Answer: 23.57 cm
Perimeter of rectangle :
$$\eqalign{ & = \left \cr & = 30\,cm \cr} $$
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 :
$$\eqalign{ & = \left( {\frac{{22}}{7} \times \frac{{15}}{2}} \right)cm \cr & = \left( {\frac{{165}}{7}} \right)cm \cr & = 23.57\,cm \cr} $$
$$\eqalign{ & = \left \cr & = 30\,cm \cr} $$
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 :
$$\eqalign{ & = \left( {\frac{{22}}{7} \times \frac{{15}}{2}} \right)cm \cr & = \left( {\frac{{165}}{7}} \right)cm \cr & = 23.57\,cm \cr} $$