Question

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$\large{\underline{\underline{\mathrm \blue{Question}}}}$

Find the minimum length in cm and correct to the nearest whole number of a thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. The width of the metal sheet is 1 m. Also, find the cost of the sheet at the rate of Rs. 56 per m. Find the area of the metal sheet required if 10% of it is wasted in cutting, overlapping etc.

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Answer 1

Solution :-

→ Radius of cylinder = r = Diameter / 2 = 20/2 = 10 cm

→ Height of cylinder = h = 35 cm .

So,

→ TSA of cylinder = 2πr(h + r) = 2 * 3.14 * 10 * (35 + 10) = 2 * 31.4 * 45 = 31.4 * 90 = 2826 cm²

now,

→ Width of metal sheet = 1 m = 100 cm

then,

→ Length of metal sheet = TSA of cylinder / Width of metal sheet = 2826/100 = 28.26 cm ≈ 28 cm (Ans.)

Now,

→ Cost of the sheet = Total area * Rate / m² = 2826 cm² * 56 = (2826/10000) * 56 = 0.2826 * 56 = Rs.15.82 (Ans.)

Now, since 10% of area of metal sheet is wasted in cutting, overlapping etc.

therefore,

→ The area of the metal sheet required = Area of metal sheet used + 10% of area of metal sheet

→ The area of the metal sheet required = 110% of area of metal sheet used

→ The area of the metal sheet required = (110/100) * 2826

→ The area of the metal sheet required = 1.1 * 2826

→ The area of the metal sheet required = 3108.6 cm² (Ans.)

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