Question

Circular place mats of diameter 8 cm are made by stamping as many circles as possible from a rectangular strip of card measuring 8 cm by 64 cm. How many mats can be made from the strip of card and what area of card is wasted?

Answer 1

Number of mats which can be made from the strip of card $=\frac{areaofstripofcard}{areaofonecircularplacemat}$

$=\frac{lb}{\pi r^2}$

$=\frac{8\times 64}{\frac{22}{7}\times 4^2}$

$=\frac{8\times 64\times 7}{22\times 16}=10.18$

Therefore possible numbers of circular place mats$=10$

Area of card which is wasted =area of 10 circular place mats

$=10\times \frac{22}{7}\times 4^2=502.85c{m}^2$