Math in real life

1) Surface Area and Volume of a Cylinder2) Heron's Formula

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Mathematics

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Area of Triangular sign board using Heron's Formula:Sides:a= 50cmb= 60cmc= 70cmTherefore, s= (a+b+c)/2 = 180/2 = 90cmwhere s is half of the perimeter of the triangle.Area of board=√(s(s-a)(s-b)(s-c)) = √(90 (90-50)(90-60)(90-70)) = √(90 ×40×30×20) = 3√10×4√10×√30×√20 = 7√10 ×√30×√20 = 542.22 cm^2 (approx.)Since there are two similar boards = 2×542.22 cm^2= 1084.44 cm^2 (approx.)

Surface area and volume of a Cylindrical Water Geyser:Dimensions:diameter = 42cmTherefore, radius = 21cmheight = 50cmVolume of cylinder = πr^2*h = 22/7×21×21×50 = 69300cm^3 = 69.3l (approx.)Surface area of cylinder = 2πr (h+r) = 2×22/7×21 (50+21) = 132×71 = 9372 cm^2 (approx.)1) I am taking the volume of this cylindrical water geyser to measure how much water it can heat at a time.2) I am taking the surface area of this cylindrical water geyser to see how much space it occupies in my house.

Cylindrical Water Geyser

Triangular sign boards