Question

Discs of a radius 4cm are cut from a rectangular plastic sheet of length 84cm and width 24 cm

Answer 1

Answer: 40

Step-by-step explanation:

Given

Radius of disc $r=4\ cm$

The dimension of the sheet is $84\times 24\ cm^2$

Area of a single disc

$\Rightarrow a=\pi r^2=\frac{22}{7}\times 4^2\\\\\Rightarrow a=\frac{352}{7}\ cm^2$

Area of sheet

$\Rightarrow A=84\times 24=2016\ cm^2$

No. of discs that can be cut off the sheet are

$\Rightarrow n=\dfrac{A}{a}=\dfrac{2016}{\frac{352}{7}}=\dfrac{2016\times7}{352}\\\Rightarrow n\approx 40$

The total area of the disc is

$\Rightarrow na=40\times\frac{352}{7}=2011.428\ cm^2$

Sheet wasted

$\Rightarrow A-na=2016-2011.428=4.57\ cm^2$