Find the total perimeter of all the petals in each of the given flowers. Class 9

Find the total perimeter of all the petals in each of the given flowers. Class 9

Question 1.

Find the total perimeter of all the petals in each of the given flowers. Class 9

Solution:

i.

Side of square = 14 cm

Radius of each arc =$\frac{14}{2}$ = 7cm

Each petal is made of 2 quarter circles

Length of one petal = 2 × $\frac{1}{4}$ × 2πr

= πr

= $\frac{22}{7}$ × 7 = 22 cm.

Number of petals = 4

∴ Total perimeter of all petals = 4 × 22

= 88 cm

∴ Total perimeter of all petals = 88 cm

ii.

Side of hexagon = 42 cm

∴ Radius of each arc = 42 cm

∵ Each petal is made of 2 arcs in regular hexagon

Each interior angle = 120°

∴ Angle subtended by each arc at centre = 60°

∴ Length of arc

$\begin{aligned} & =\frac{\theta}{360} \times 2 \pi r \\ & =\frac{60}{360} \times 2 \pi r \\ & =\frac{1}{6} \times 2 \times \frac{22}{7} \times 42 \\ & =\frac{2}{6} \times \frac{22}{7} \times 42 \\ & =\frac{1}{3} \times \frac{22}{7} \times 42 \\ & =\frac{1}{3} \times 132=44 \mathrm{~cm}\end{aligned}$

∵ Total petals = 6

∴ Total arc's = 6 × 2 = 12 cm.

∴ Total perimeter of petals = 12 × 44 = 528 cm.

∴ Total perimeter of petals = 528 cm.