QUESTION 7
Easy
Find the total perimeter of all the petals of the given flowers.
SOLUTION
1
(i)
Side of square \(= 14\,cm\)
Radius of circle, \(r = \frac{14}{2}\,=7\,cm\)
Circumference of 2 full circles \(= 2 × 2πr \,= 4 × \frac{22}{7} × 7\,= 88\,cm\)
Total perimeter of the petals = 88 cm.
Radius of circle, \(r = \frac{14}{2}\,=7\,cm\)
Circumference of 2 full circles \(= 2 × 2πr \,= 4 × \frac{22}{7} × 7\,= 88\,cm\)
Total perimeter of the petals = 88 cm.
2
(ii)
Radius \(= 42\,cm\)
Length of one arc \(= \frac{60}{360} × 2πr \,= \frac{1}{6} × 2 × \frac{22}{7} × 42\,= 44\,cm\)
So, length of 12 arcs \(= 12 × 44\,= 528\,cm\)
The total perimeter of the petals is 528 cm.
Length of one arc \(= \frac{60}{360} × 2πr \,= \frac{1}{6} × 2 × \frac{22}{7} × 42\,= 44\,cm\)
So, length of 12 arcs \(= 12 × 44\,= 528\,cm\)
The total perimeter of the petals is 528 cm.
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Final Answer :
(i) 88 cm
(ii) 528 cm
Concept Note
(i) The figure is a square of side 14 cm.
The centres of the circles are the midpoints of the sides.
Each petal is made up of two quarter-circle arcs.
Since there are 4 petals, the total perimeter consists of eight quarter-circle arcs.
2 quarter-circle arcs = one semicircle
8 quarter-circle arcs = 4 semicircles = 1 complete circle
(ii)The figure is a regular hexagon with side 42 cm.
The centres of the arcs are the vertices of the hexagon.
Each petal consists of 2 arcs. There are 6 petals. Hence, there are 12 arcs in total.
In a regular hexagon. the angle at the centre of each arc is 60°, so each arc is a 60° arc of a circle.