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प्रश्न
The ratio of the radius and height of a cylinder is 2:3. If its volume is 12,936 cm3, find the total surface area of the cylinder.
उत्तर
The ratio of the radius and height of a cylinder = 2:3
Let the radius of the cylinder be 2x and the height of the cylinder be 3x.
Volume of the cylinder = 12936 cm3
∵ Volume of a cylinder = πr2h
∴ `12936 = 22/7 xx (2x)^3 xx 3x`
⇒ `12936 = 22/7 xx 4x^2 xx 3x`
⇒ `12936 = 264/7 x^3`
⇒ `x^3 = (12936 xx 7)/264 = 49 xx 7`
⇒ x3 = 7 × 7 × 7 = (7)3
⇒ x3 = (7)3
∴ x = 7
So, radius 2x = 2 × 7 = 14 cm and height = 3x = 3 × 7 = 21 cm
The total surface area of the cylinder = 2πr(r + h)
= `2 xx 22/7 xx 14(14 + 21)`
= `(44 xx 14)/7 xx 35`
= 44 × 14 × 5
= 3080 cm2
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