Question

Q 44. Consider a cylinder with a diameter of its base as 20 cm and height 4 cm. If "x" cm is added to either radius or height to get the same
increase in the volume of the cylinder, then the value of "x" is:

Answer 1

Step-by-step explanation:

A) 5 cm

Description for Correct answer:

Let the required increase = x cm

⇒π(10+x)2×4=π×102×(4+x)

100+x2+20x=25(4+x)

x2+20x+100=100+25x

x2−5x=0

x−5=0

x=5

∴ Required increase = 5 cm

Answer 2

The value of x is 5.

Given:

Diameter, d = 20 cm

Radius, r = 20/2 cm

r = 10 cm

height, h = 4 cm

"If "x" cm is added to either radius or height to get the same

increase in the volume of the cylinder"

To Find:

The value of x.

Solution:

The volume of the cylinder, V = πr²h -------(1)

1) In the first case, 'x' cm is added to the base radius of the cylinder.

r = x+10, h = 4 cm, π = 3.14 substitute in equation(1)

V = 3.14×(x+10)²×4

  = 12.56×(x+10)²

  = 12.56(x²+20x+100)

  = 12.56x²+251.2x+1256   ----------(2)

2) In the second case, 'x' cm is added to the height of the cylinder.

r = 10 cm, h = x+4, π = 3.14  substitute in equation(1)

V = 3.14×10²×(x+4)

   = 314(x+4)

   = 314x+1256  ----------(3)

It is given in both cases the volume of the cylinder is the same.

So equation(2) is equal to equation(3)

12.56x²+251.2x+1256 = 314x+1256

12.56x² - 62.8x = 0

x(12.56x-62.8) = 0

12.56x-62.8 = 0 or x = 0 (not considered as x can't be zero)

12.56x = 62.8

x = 62.8/12.56

x = 5

Therefore, The value of x is 5.

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