Question

Shalini has to cut out circe 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

Given $d=1\frac{1}{4}=\frac{5}{4}\Rightarrow r=\frac{5}{8}Cm.$

Area of circle $=\pi r^2=\pi {\left(\frac{5}{8}\right)}^2=\frac{25\pi }{64}C{m}^2.$

Area of strip $=\left(8\frac{3}{4}\right)\times \left(1\frac{1}{4}\right)=\frac{35}{4}\times \frac{5}{4}$

$=\frac{175}{16}C{m}^2=10.9375C{m}^2.$

diameter of circle = breadth of strip.

of Circles $=\frac{Lengthofstrip}{diameterofcircle}=\frac{\left(35/4\right)}{\left(5/4\right)}$

$=7$

Total area of circles $=7\times \frac{25\pi }{64}=8.590c{m}^2.$

Area wasted = strip area - total area of circles

$=2.343c{m}^2$