A rectangular sheet metal measures 12 cm by 8 cm. Four quadrants of circle of radius 2 cm each are cut away at the corners. Find the area of the remaining portion.
Answers
Given data : A rectangular sheet metal measures 12 cm by 8 cm. Four quadrants of circle of radius 2 cm each are cut away at the corners.
Solution: a/c to given data
- length of the sheet = 12 cm
- breadth of the sheet = 8 cm
- radius of each quadrant of circle = 2 cm
firstly we have to find out area of rectangular metal sheet.
Formula : area of rectangle = length * breadth
⟹ area of the sheet = 12 * 8
⟹ area of the sheet = 96 cm²
Now, we have to find out area of each quadrant, so now by formula : area of circle = πr²
There are four quadrant hence
⟹ Area of one quadrant = 1/4 πr²
⟹ Area of one quadrant = 1/4 * 22/7 * 2²
⟹ Area of one quadrant = 22/28 * 4
⟹ Area of one quadrant = 22/7 cm²
Now,
⟹ Area of four quadrant = 4 * 22/7
⟹ Area of one quadrant = 44/7 cm²
To area of remaining portion,
⟹ Area of remaining portion = area of the sheet - area of quadrant
⟹ Area of remaining portion = 96 - 22/7
⟹ Area of remaining portion = (672 - 22)/7
⟹ Area of remaining portion = 650/7
⟹ Area of remaining portion = 92.8571 cm².
Answer : Hence, the area of remaining portion is 92.8571 cm².
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