In the following figure, there are three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate:
(i)the area of the shaded region
(ii)the cost of painting the shaded region at the rate of 25 paise per cm² , to the nearest rupee.
Answers
Answer:
Area of shaded region is 13.275 cm² and the cost of painting the Shaded Region is ₹ 3 .
Step-by-step explanation:
Given :
Three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm.
(i) Area of shaded region ,A = Area of the semicircle with diameter 9 cm - Area of two semicircles with radius 3 cm - area of the circle with centre D + area of semicircle with radius 3 cm
A = 1/2 π(9/2)² - 2 × 1/2 π(3/2)² - π(4.5/2)² + 1/2 π(3/2)²
[Area of semicircle = 1/2 πr² and Area of circle = πr² ]
A = 1/2 π(4.5)² - π(1.5)² - π(2.25)² + 1/2 π(1.5)²
A = 1/2 π(4.5)² - π(1.5)² + 1/2 π(1.5)² - π(2.25)²
A = 1/2 π(4.5)² - 1/2 π(1.5)² - π(2.25)²
A = 1/2π( 4.5² - 1.5² ) - π 2.25²
A = ½ π (20.25 - 2.25) - π×5.0625
A = ½ π(18) - π ×5.0625
A = 9π - π 5.0625
A = π(9 - 5.0625)
A = π × 3.9375
A = 22/7 × 3.9375
A = 0.5625 × 22
A = 12.375 cm²
Area of shaded region = 13.275 cm²
(ii) Cost of painting 1 cm² Shaded Region = 25 p
Cost of painting 13.275 cm² Shaded Region = 25 p × 13.275
= 309.375 paise
= ₹ 309.375 /100
= ₹ 3 (nearest rupee)
Cost of painting the Shaded Region = ₹ 3 .
Hence, the cost of painting the Shaded Region is ₹ 3 .
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Refer the attached picture.
