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The Ratio Between the Radius of the Base and the Height of a Cylinder is 2 : 3. If Its Volume is 1617 Cm3, the Total Surface Area of the Cylinder is - Mathematics

MCQ

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If its volume is 1617 cm3, the total surface area of the cylinder is

Options

  • 308 cm2

  • 462 cm2

  •  540 cm2

  • 770 cm2

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Solution

770 cm2

Let the common multiple be x.

Let the radius of the cylinder be 2x cm and its height be 3x cm.

Then, volume of the cylinder `= pi"r"^2"h"`

`= 22/7xx(2x)^2xx3x`

Therefore,

`22/7xx(2x)^2xx3x=1617`

`=> 22/7xx4x^2xx3x = 1617`

`=>22/7xx12x^3=1617`

`=x^3 = (1617xx7/22xx1/12)`

`= x^3 = (7/2xx7/2xx7/2)`

`=x^3 = (7/2)^3`

`=> x= 7/2`

Now, r = 7 cm and  `"h" = 21/2 "cm"`

Hence, the total surface area of the cylinder

`=(2pi"rh"+2pi"r"^2)`

`= 2pi"r"(2xx22/7xx7xx35/2)"cm"^2`

= 770 cm

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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Multiple Choice Questions | Q 54 | Page 923
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