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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

Is there an error in this question or solution?
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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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