PRACTICE PROBLEMS ON CONVERTING CIRCLE FROM ONE SHAPE TO ANOTHER

Problem 1 :

A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form of a square, then its area will be

(a)  3520 cm²  (b)  6400 cm²  (c)  7744 cm²   (d)  8800cm²

Solution

Problem 2 :

If a wire is bent into the shape of a square, then the area of the square is 81 cm². When wire is bent into a semi-circular shape, then the area of the semi-circle will be

(a)  22 cm²  (b)  44 cm²   (c)  77 cm²   (d)  154 cm²

Solution

Problem 3 :

The circumference of a circle is 100cm. The side of a square inscribed inthe circle is

(a)  50√2 cm   (b)  100/π cm   (c)  50√2/π cm  (d)  100√2/π cm

Solution

Problem 4 :

If an arc of a circle forms 90^º at the centre of the circle, then the ratio of its length to the circumference of the circle is 

(a)  1 : 4    (b)   3 : 4   (c)  1 : 3   (d)  2 : 3

Solution

Problem 5 :

The area of a circle is 220cm². The area of square inscribed in it is

(a)  49 cm²  (b)  70 cm²  (c)  140 cm²  (d)  150 cm²

Solution

Problem 6 :

The area of the circle that can be inscribed in a square of side 6 cm is

(a)  36 π cm²   (b)   18 π cm²  (c)  12 π cm²   (d)   9 π cm²

Solution

Problem 7 :

The area of the square that can be inscribed in a circle of radius 8 cm is

(a)  256 cm²   (b)   128 cm²  (c)  64√2 cm²   (d)   64 cm²

Solution