 # NCERT Exemplar Solutions Class 8 Mathematics Solutions for Rational Numbers - Exercise in Chapter 1 - Rational Numbers 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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