“The ratio between the radius of the base and the height of a cyclinder is 2:3 find the total surface area of the cyclinder if it's volume is 1617 cubic cm”.
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Soln:
Let Base radius = 2K and Height = 3K
Volume of Cylinder = πr²h = 1617 cm³
⇒ (22/7) × (2K)² × (3K) = 1617
⇒ K³ = (1617 × 7) / (22 × 3 × 4) = 42.875
⇒ K = 3.5
Hence, Base radius = 2 × 3.5 = 7 cm and Height = 3 × 3.5 = 10.5 cm
Total Surface area of the cylinder = 2πr(r + h) = 2 × 22/7 × 7 × 17.5 = 2 × 22 × 17.5 = 770 cm²
Let Base radius = 2K and Height = 3K
Volume of Cylinder = πr²h = 1617 cm³
⇒ (22/7) × (2K)² × (3K) = 1617
⇒ K³ = (1617 × 7) / (22 × 3 × 4) = 42.875
⇒ K = 3.5
Hence, Base radius = 2 × 3.5 = 7 cm and Height = 3 × 3.5 = 10.5 cm
Total Surface area of the cylinder = 2πr(r + h) = 2 × 22/7 × 7 × 17.5 = 2 × 22 × 17.5 = 770 cm²
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