Find the minimum length in cm and correct to nearest whole number of the thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. Given that 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 metal sheet required, if 10% of it is wasted in cutting, overlapping, etc.

Question

Find the minimum length in cm and correct to nearest whole number of the thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. Given that 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 metal sheet required, if 10% of it is wasted in cutting, overlapping, etc.

KnowledgeBoat · Accepted Answer

Given, Height of the cylinder box (h) = 35 cm Base radius of the cylinder box (r) = = 10 cm Width of metal sheet = 1m = 100 cm Area of metal sheet required = Total surface area of the box ⇒ Length x width = 2πr(r + h) ⇒ Length x 100 = 2 x x 10(10 + 35) ⇒ Length x 100 = 2 x x 10 x 45 ⇒ Length = = 28.28 cm ≈ 28 cm (correcting to the nearest whole number) Thus, Area of metal sheet = length x width = 28 x 100 = 2800 cm² = = 0.28 m². So, the cost of the sheet at the rate of ₹ 56 per m² = ₹ (56 x 0.28) = ₹ 15.68 Let the total sheet required be x. Then, x - 10 % of x = 2800 cm ⇒ = 2800 ⇒ = 2800 ⇒ = 2800 ⇒ = 2800 ⇒ ⇒ x = 3111.11 cm² ≈ 3111 cm² (correcting to the nearest whole number) Hence, length = 28 cm, cost of sheet = ₹15.68 and area of sheet required = 3111 cm².

Mathematics

Mensuration

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