A child tries to draw the flag with inner white circle of radius2.0 cm and inner gold band of width 1cm. The outer white band (ring) of width 3cm is divided into 8 equal regions by golden strokes and an outer gold band of width 2cm. i) Calculate the area of inner white circle. ii) Find the area of inner gold band of width 1cm. iii) Calculate the area of each of 8 white regions included between golden strokes (Assume that each golden stroke has negligible thickness) iv) Find the area of outer gold band of width 2cm. v) the child tries to decorate the border by using red satin ribbon. What is the length of ribbon required if flag is 15cm long and12 cm wide. (Give your answer in π )
Answers
Given : A child tries to draw the flag with inner white circle of radius 2.0 cm and inner gold band of width 1cm. The outer white band (ring) of width 3cm is divided into 8 equal regions by golden strokes and an outer gold band of width 2cm
flag is 15cm long and 12 cm wide, the child tries to decorate the border by using red satin ribbon.
To Find :
i) Calculate the area of inner white circle.
ii) Find the area of inner gold band of width 1cm.
iii) Calculate the area of each of 8 white regions included between golden strokes (Assume that each golden stroke has negligible thickness)
iv) Find the area of outer gold band of width 2cm.
v) the length of ribbon required if
Solution:
area of circle = π ( Radius)²
inner white circle of radius2.0 cm
=> inner white circle area = π ( 2)² = 4π cm²
Width of inner gold band = 1 cm
Radius = 2 + 1 = 3 cm ( including white circle and gold band)
Area of inner white circle and inner gold band = π ( 3)² = 9π cm²
area of inner gold band of width 1cm. = 9π - 4π = 5π cm²
The outer white band of 3 cm width
Hence radius = 3 + 3 = 6 cm
Area of outer and inner white circle + inner gold band = π ( 6)² = 36π cm²
area of 8 white regions included between golden strokes = 36π - 9π
= 27π cm²
Area of each white region = 27π/8 = 3.375π cm²
Area of outer gold band width 2 cm = π(6 + 2)² - π6²
= 28π cm²
length of ribbon required if flag is 15cm long and 12 cm wide.
= 2 ( 15 + 12)
= 54 cm
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