Page 146 - Maths Skills - 7
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144 Maths
Example 3: Find the area of a circle whose radius is 7 cm.
Solution: Area of a circle = pr = 22 × (7 cm) = 154 cm .
2
2
2
7
Example 4: Find the area of a circle inscribed in a square of side 7 m.
Solution: From Fig., it is clear that the diameter of the circle is 7 m.
7
\ Radius = m
2
2
7
7
\ Area of the circle = pr = 22 × 7 m = 22 × × m = 38.5 m .
2
2
2
7 2 7 2 2
Example 5: A rectangular park is bounded by semicircles at the ends
each of radius 7 m as shown in Fig. If the length of the
rectangle is 65 m, then find the perimeter of the park.
Solution: Perimeter of the park = Measure of length AB + Measure of length BCD + Measure of length DE
+ Measure of length EFA.
1 22 1 22
2
2
= 65 m + ×× × 7 + 65 m + ×× × 7
2 7 2 7
= 65 m + 22 m + 65 m + 22 m = 174 m
1
[Q Measure of length BCD = EFA = circumference of the circle]
2
\ Perimeter of the park = 174 m.
Example 6: A square plate of edge 5 cm has a circular hole of area 16 cm . Find the area of the remaining plate.
2
Solution: The area of the remaining portion of the square plate will be the shaded
portion as shown in Fig.
\ Area of the shaded portion = Area of a square – Area of a circular hole
= (25 – 16) cm = 9 cm 2
2
\ Area of the remaining plate = 9 cm .
2
Example 7: Two concentric circles have the radii 12 cm and 8.5 cm respectively. Calculate the area of the space
enclosed by these two circles. [Use p = 3.14]
Solution: Let the two circles of radii (R) 12 cm and (r) 8.5 cm be as shown in Fig.
Therefore, area of the space enclosed by these two circles = Area of shaded region
= pR – pr = p(R – r ) = p(R – r) (R + r)
2
2
2
2
= 3.14 × (12 – 8.5) (12 + 8.5) = 3.14 × 3.5 × 20.5 = 225.295 cm 2
Fig. 11.32
Exercise 8.6
1. Find the area covered by a circular plate whose radius is 4.9 cm.
2. The area of a circular park is 525 sq m. Find the cost of levelling the field at ` 5 per m .
2
3. Find the area of a circle whose radius is 28 cm.
4. Find the radius of the circular park if area of the park is 7546 sq m.
