Question

Circular discs, each of radius 4 cm, are to be cut from a rectangular sheet of card which
is 24cm long by 16 cm wide. Calculate
(a) the maximum number of discs which can be cut.
(b) the percentage, to 3 significant figures, of the card which is
not used.​

Answer 1

Solution :-

→ Radius of disc = 4 cm .

so,

→ Diameter of disc = 4 * 2 = 8 cm .

now, we can say that,

• we need an (8 * 8) square cut outs out of 24 * 16 rectangular sheet to make a circle .

then,

→ 8 * 8 square = 1 circle .

so,

→ Total circles = (24 * 16) / (8 * 8) = 6 circles .

therefore, Maximum number of discs than can be cut are 6 discs.

Now,

→ Area of rectangular sheet = 24 * 16 = 384 cm².

→ Area of 6 discs of 4 cm = 6 * 3.14 * (4)² = 301.44 cm².

then,

→ Card which is not used = 384 - 301.44 = 82.56 cm².

hence,

→ Required % = (82.56 * 100) / 384 = 21.5% (Ans.)

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