The ratio between the radius of the base and height of a cylinder is 2 : 3. If its volume is 1617 cm³ , find the total surface area of the cylinder.
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Let, the radius of the cylinder be 'r' and the height of the cylinder be 'h'.
Given : r : h = 2 : 3
Let radius = 2x cm and height = 3x cm
Volume of cylinder = πr²h
Volume of cylinder = 1617 cm³ [ Given]
1617= 22/7 × (2x)² × 3x
1617= 22/7 × 4x² × 3x
1617 = 22/7 × 12x³
1617 × 7 = 22 × 12 × x³
x³ = (1617 × 7)/22 × 12
x³ = 343/8
x = ³√343/8
x = 7/2
x = 3.5 cm
Now, radius, r = 2x = 2 x 3.5 = 7 cm
Height = 3x = 3 x 3.5 = 10.5 cm
Now,
Total surface area of cylinder = 2πr(h + r)
= 2 x 22/7 x 7(10.5 + 7)
= 44 × 17.5
= 770 cm²
Hence, the total surface area of the cylinder is 770 cm².
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