Question

Shalini has to cut out circles of diameter 1 1/4 cm from an aluminium strip of dimensions 8 3/4 cm by 1 1/4 cm. How many full circles can Shalini cut? Also calculate the wastage of the aluminium strip.

Answer 1

diameter = 1 1/4 = 1.25 cm

Therefore , radius = 1.25/2

Area of one circle =  $\pi r ^{2}$ = (22/7) *  (1.25/2)² = 1.22767857143

area of the aluminium sheet =

Answer 2

7 full circles can shalini cut and the wastage of the aluminum strip is $\bold{K=\frac{75}{32} C m^{2}}$.

Aluminium Strip  

Length $=8 \frac{3}{4}=\frac{35}{4}$

Breadth $=1 \frac{1}{4}=\frac{5}{4}$

Area of rectangle $=\text {Length} \times {Breadth}$

$=\frac{35}{4} \times \frac{5}{4}=\frac{175}{16} \mathrm{Cm}^{2}$

And Circle  

Diameter $=1 \frac{1}{4}=\frac{5}{4}$

Radius $=\frac{5}{8}$

Area of circle $=\pi \times r^{2}=\frac{25 \pi}{64} C m^{2}$

If we observe, Diameter of circle is equal to Breadth of Aluminum strip Which implies.

Number circles = Length of aluminum strip / Diameter of circle

$N=\frac{\left(\frac{35}{4}\right)}{\left(\frac{5}{4}\right)}=7$

And area of aluminum strip $=N \times \text { area of circles }+ { wastage}$

Let us assume Wastage is K

$\frac{175}{16}=7 \times\left(\frac{25 \pi}{64}\right)+K$

Substitute $\pi=\frac{22}{7}$

$\frac{175}{16}=\left(7 \times \frac{25}{64} \times \frac{22}{7}\right)+K$

$\frac{175}{16}=\left(25 \times \frac{11}{32}\right)+K$

$\frac{175}{16}=\frac{275}{32}+K$

$K=\frac{175}{16}-\frac{275}{32}$

$K=\frac{75}{32} C m^{2}$