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Mathematics

A cylindrical container is to be made of tin sheet. The height of the container is 1 m and its diameter is 70 cm. If the container is open at the top and the tin sheet costs 300 per m2, find the cost of the tin for making the container.

Mensuration

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Answer

Since, container is open at the top hence total surface area of container (S) = curved surface area + area of base.

Radius of container = 702\dfrac{70}{2} = 35 cm = 0.35 m.

⇒S=2πrh+πr2=2×227×0.35×1+227×0.35×0.35=2×22×0.5+22×0.5×0.35=22+3.85=25.85 m2\Rightarrow S = 2πrh + πr^2 \\[1em] = 2 \times \dfrac{22}{7} \times 0.35 \times 1 + \dfrac{22}{7} \times 0.35 \times 0.35 \\[1em] = 2 \times 22 \times 0.5 + 22 \times 0.5 \times 0.35 \\[1em] = 22 + 3.85 \\[1em] = 25.85 \text{ m}^2

Cost of 1 m2 sheet = ₹ 300.

Total cost = ₹ 300 × 25.85 = ₹ 775.50

Hence, the cost of tin for making the container is ₹ 775.50

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