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

Breadth of the circle = Diameter of one circle `1 1/4` cm = `5/4` cm

Length of aluminium strip = `8 3/4` cm = `35/4` cm

∴ Number of full circles cut from the aluminium strip

= `35/4 ÷ 5/4`

= `35/4 xx 4/5`

= 7

Hence, the number of circle 7.

Now, diameter of circle = `5/4` cm

Radius of circle = `5/(4 xx 2) = 5/8` cm

Now, area to be cut by one circle

= πr²

= `22/7 xx (5/8)^2`

= `22/7 xx 25/64` cm²

∴ Area to be cut by 7 full circles

= `7 xx 22/7 xx 25/64`

= `(22 xx 25)/64`

Also, area of the aluminium strip

= Length × Breadth

= `35/4 xx 5/4` cm²

∴ Wastage of aluminium strip

= `(35/4 xx 5/4) - ((22 xx 25)/64)`

= `175/16 - 550/64`

= `(700 - 550)/64`

= `150/64`

= `75/32`

= `2 11/32` cm²

Hence, the wastage of aluminium strip is `2 11/32` cm².