Question

1). from the circular card sheet of radius is 28 cm , two circles of radii 7 cm and a rectangle of length 3 cm and breadth 2 cm removed , find the area of remaining sheet

2). a horse is toed to a. pole with 9.8 m long string. find the area where the horse can graze

3). the area of two circle are in ratio 9:16 . find the ratio of their circumference .

4). area of circle is 75 . 46 sq. m , find its diameter

5) a circular flowerbed is surrounded by path 5 m wide , the diameter of flowerbed is 56 m , what is the area of path

Answer 1

1.area of circular card sheet =πr^2
=22/7× 28×28
=2464 sq.cm
Now, area of two smaller circles that was cut
=2×π ×r^2
=2×22/7×7×7
=308sq.cm
Then, area of rectangle that was cut= L×B
=3×2
=6sq.cm

hence,the area of remaining sheet = area of circular card sheet - area of two smaller circles+area of rectangle
= 2464-308+6
=2152sq.cm

2. area covered by the horse is in the form of circle so we will do area of circle= πr^2
=22/7×9.8×9.8
=301.84sq.cm

3. ratio of area is9:16
πR1^2/πr2^2=9/16
R1/r2=√9/√16
R1/r2=3/4
ratio of their perimeter
=2πR/2πr=2×3/2×4=6/8=3/4

4. area of circle=75.46
πr^2=75.46
r^2=75.46/π
r^2=75.46×7/22
r^2=2401
r=√2401
r=49
d=2r
d=2×49
d=98cm

5. area of flower bed= πr^2=22/7×28×28
=2464sq.cm
area of bigger circle= πr^2
r=28+5=33cm
=22/7×33×33
=3422.57sq.cm
area of path=ar of bigger circle -area of smaller circle
= 3422.57-2464
958.57sq.cm