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Question 142
Shaline has to cut out circles of diameter 114 cm from an aluminium strip of dimensions 834 cm by 114 cm. How many full circles can Shalini cut? Also, calculate the wastage of the aluminium strip.


Solution

Breadth of the circle
= Diameter of one circle
=114 cm=54 cm

Length of aluminium strip =834 cm=354 cm

Number of full circles cut from the aluminium strip
=354÷54=354×45=7

Hence, we can cut 7 full circles from given aluminium strip.


Now diameter of circle
=54 cm

Radius of circle
=54×2=58 cm

Now, area to be cut by one circle
=πr2=227×(58)2
=227×2564 cm2

Area to be cut by 7 full circles =7×227×2564=22×2564

Also, area of the aluminium strip = Length * Breadth
=354×54 cm2

Wastage of aluminium strip
=(354×54)(22×2564)

=1751655064

=70055064=15064

=7532=21132 cm2

Hence, the wastage of aluminium strip is 21132 cm2

Mathematics
NCERT Exemplar
Standard VIII

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