Question

Question 142
Shaline has to cut out circles of diameter $1\frac{1}{4}cm$ from an aluminium strip of dimensions $8\frac{3}{4}cm$ by $1\frac{1}{4}cm$. How many full circles can Shalini cut? Also, calculate the wastage of the aluminium strip.

Answer 1

Breadth of the circle
= Diameter of one circle
$=1\frac{1}{4}cm=\frac{5}{4}cm$

Length of aluminium strip $=8\frac{3}{4}cm=\frac{35}{4}cm$

$\therefore$ Number of full circles cut from the aluminium strip
$=\frac{35}{4}÷\frac{5}{4}=\frac{35}{4}\times \frac{4}{5}=7$

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


Now diameter of circle
$=\frac{5}{4}cm$

Radius of circle
$=\frac{5}{4\times 2}=\frac{5}{8}cm$

Now, area to be cut by one circle
$=\pi r^2=\frac{22}{7}\times {\left(\frac{5}{8}\right)}^2$
$=\frac{22}{7}\times \frac{25}{64}c{m}^2$

$\therefore$ Area to be cut by 7 full circles $=7\times \frac{22}{7}\times \frac{25}{64}=\frac{22\times 25}{64}$

Also, area of the aluminium strip = Length * Breadth
$=\frac{35}{4}\times \frac{5}{4}c{m}^2$

$\therefore$ Wastage of aluminium strip
$=(\frac{35}{4}\times \frac{5}{4})-\left(\frac{22\times 25}{64}\right)$

$=\frac{175}{16}-\frac{550}{64}$

$=\frac{700-550}{64}=\frac{150}{64}$

$=\frac{75}{32}=2\frac{11}{32}c{m}^2$

Hence, the wastage of aluminium strip is $2\frac{11}{32}c{m}^2$