Monday, 23 October 2023

CIRCLE (MENSURATION)

) Find the circumference and the area of a circle of 
a) radius 21 cm.        1386cm²
b) diameter 14cm.          154cm2

) if the circumference of a circle is 132 cm, find its radius and area.    21cm, 1386cm²

) If the area of a circle is 15400 cm², find its radius and circumference.   70cm, 440cm

) if the wheel of a bicycle has a diameter of 84cm, find
a) the distance travelled by the cyclist after one rotation of the wheel.    264cm
b) the number of rotations of the wheel if the cyclist covers a distance of 1.65 km.    625

) A 72cm long piece of wire is bent into the form of a semi circular are bounded by its diameter. Find the radius.         14cm

) A metal wire is bent in the shape of a square of area 484cm². If the same wire is bent to form a circle, find the area enclosed.       616cm²

) A wire is in the shape of a circle of area 3850 cm². If the same wire is bent in the form of a square, find the area of the square.     3025cm²

) A circular park of diameter 30 m is surrounded by a circular path of uniform width 5 m. Find the area of the path.        550m²

) The area of the ring between two concentric circles is 990 cm². Find the radii of the two circles if their sum is 35cm.        22cm, 13cm

) A garden is made up of a rectangular patch of grass and two semi-circular ponds, as shown in the figure. If the length and width of the rectangular patch are 24 m and 14 m respectively,
 Calculate 
a) the perimeter of the garden.       92m
b) the total area of the garden.        490m²

)  A rectangle of length 35 cm and width 28cm has a semicircle cut out from each of its two sides, as shown. 
Find the area of the shaded portion.      364cm²

) Find the circumference and area of a circle of 
a) radius 14 cm.        88cm, 616cm²
b) radius 2.1 m.        13.2m, 13.86m²
c) diameter 35 cm.      110cm, 962.5cm²
d) diameter 77 cm.     242cm, 4658.5 cm²

) Find the radius of a circle and area if its circumference is
a) 176cm.      28cm, 2464cm²
b) 11 meter.    1.75m, 9.625m²
c)  16πcm.         8cm, 64π cm²

) Find the diameter of a circle and its circumference if its area is
a) 6.16 m².      2.8m, 8.8m
b) 394.24cm².         22.4cm, 70.4cm
c) 25π cm.      10cm, 10π cm

) A bicycle wheel is 1 m 26cm in diameter. Calculate 
a) the distance travelled in one rotation of the wheel.       Em 96cm
b) the number of rotations of the wheel needed to cover 1.98 km.      500

) A 54 cm long piece of wire is bent into the shape of a semi-circular are bounded by its diameter. Find its radius.          10.5cm

) A wire is bent in the form of a square of area 1936 cm². If the same wire is bent to form a circle, find the radius of the circle and area enclosed.        28cm, 2464cm²

) A wire is in a circular shape of area 5544 cm². If the same wire is bent in the shape of a square, find the length of a side of the square and its area.      66cm, 4356 cm²

) A circular pond of diameter 28 m is surrounded by a path 7m wide . Find the area of the path.       770m²

) Find the area of a 2m wide circular path surrounding a circular plot of radius 20m.   264m²

) The area of the ring between two concentric circles is 3168 cm². Find the radius of the two circles if
a) their sum is 42cm.       33cm
b) their difference between us 28 cm.      9cm 

) How many plants can be planted in a circular garden of circumference 26.40 km if a space of 600 cm² is to be allowed for each plant ?      924

) A circle of circumference 88cm is cut out of a square sheet of paper of side 30 cm. What is the area of the paper left ?        284cm²

) If ABCD is a rectangle, 
find the area of the shaded portion.      45.84 m²

) Two semi-circle of equal radii are cut out of a semi-circular piece of cardboard. 
Find the area of the shared portion.         38.5 m²

) A rectangle encloses four circles. The radius of each circle is 7cm. 
Calculate the area of
a) rectangle.         784 cm²
b) the shaded portion.           168 cm²

) Find area of the shaded portion formed by a semi-circle placed above the square.   
                                                 68.25 cm²

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