If the Height of a Cylinder is Doubled, by What Number Must the Radius of the Base Be Multiplied So that the Resulting Cylinder Has the Same Volume as the Original Cylinder? - Mathematics

MCQ

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?

Options

• 4

• $\frac{1}{\sqrt{2}}$

• 2

• $\frac{1}{2}$

Solution

Let V1 be the volume of the cylinder with radius r1 and height h1, then

V_1 = pir_1^2 h_1……. (1)

Now, let V2 be the volume after changing the dimension, then

 r_2 = xr_1 , h_2 = 2h_1

So,

V_2 = pi r_2^2 h_2 = pi xx (xr_1)^2 xx 2h_1

⇒ V_2 = 2 xx pi  x^2  r_1^2  h_1

It is given that V1 =V2Therefpre,

V_1 = V_2

⇒ pi r_^2 h_1 = 2 pi x^2  r_1^2 h_1

⇒ x^2  = 1/2 r_1^2

⇒ x = 1/sqrt(2) r_1

Concept: Surface Area of Cylinder
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Exercise 19.4 | Q 14 | Page 29

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