A closed cylindrical water tank having 7 m radius and 3 m height is constructed on land. Find the cost of painting it at the rate of \( ₹ 10 \) per \( \mathrm{m}^{2} \).
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To find the cost of painting the cylindrical water tank, we first need to calculate its surface area. The total surface area of a closed cylinder is given by the formula: \[ \text{Total Surface Area} = 2\pi r(h + r) \] where \( r \) is the radius and \( h \) is the height. Here, \( r = 7 \) m and \( h = 3 \) m. Calculating this gives: \[ \text{Total Surface Area} = 2\pi(7)(3 + 7) = 2\pi(7)(10) = 140\pi \approx 439.82 \, \mathrm{m}^2 \] Now, to find the cost of painting, we multiply the surface area by the rate of painting per square meter: \[ \text{Cost} = 439.82 \, \mathrm{m}^2 \times ₹ 10 \approx ₹ 4398.20 \] So, the approximate cost of painting the tank is ₹ 4398.20. Did you know that cylindrical shapes are not just useful for water tanks but also vital in various industries? From large storage silos in agriculture to oil tanks and even skyscrapers, this shape optimizes space and stability. Engineers and architects often harness the properties of cylinders to design structures that efficiently manage volume and withstand pressure. If you ever find yourself in the swimming pool business or considering a DIY project, remember that designing cylindrical tanks can save on materials and space. Just ensure to account for the thickness of the tank's walls and additional features like access hatches. And, always avoid common pitfalls like incorrect measurements or forgetting to include drainage systems that could lead to headaches later on!
