Shalini has to cut out circles of diameter 1¼ cm from an aluminum strip of dimensions 8¾ cm by 1¼ cm. How many full circles can Shalini cut? Also calculate the wastage of the aluminum strip.
From the question it is given that,
Diameter of the circle = Breadth of the aluminium strip 1¼ cm = 5/4 cm
Length of aluminium strip = 8¾ cm = 35/4 cm
∴The number of full circles cut from the aluminum strip = (35/4) ÷ (5/4)
= (35/4) × (4/5)
= (7/1) × (1/1)
= 7 circles
Radius of circle = (5/ (4 × 2)) = 5/8 cm
Area to be cut by one circle = πr^2
= (22/7) × (5/8)^2
= (22/7) × (25/64) cm^2
Now, area to be cut by 7 full circles = 7 × (22/7) × (25/64)
= (22 × 25)/64
= 550/64 cm^2
Area of the aluminum strip = length × breadth
= (35/4) × (5/4) cm^2
= (175/16) cm^2
∴The wastage of aluminum strip = (175/16) – (550/64)
= (700 - 550)/64
= 150/64
= 75/32 cm^2
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