Question

एक गोले के त्रिज्या की 20% घटाने पर उसका आयतन कितना घटेगा

Answer 1

Answer:

48.8 %

Step-by-step explanation:

Given Reducing the radius of a sphere by 20%, its volume will decrease by

Let radius be r.

So volume will be 4πr^3/3

Now radius is decreased by 20% we get

radius = r - 20 x r/100

          = r - r/5

        = 4 r/5

Now volume is 4π r^3/3

             = 4π/3(0.8r)^3

             = 0.512 x 4πr^3/3

Now increase in volume is

  0.512 x 4πr^3/3 - 4πr^3 x 100 / 4πr^3/3

 0.512 - 1  x 100

  - 0.488 x 100

  = 48.8%

Answer 2

Answer:

एक गोले के त्रिज्या की 20% घटाने पर उसका आयतन 48.8 % घटेगा

Step-by-step explanation:

त्रिज्या = R

आयतन = (4/3)πR³

20% घटाने पर त्रिज्या  = R - (20/100)R = 0.8R

आयतन 20% त्रिज्या घटाने पर = (4/3)π((0.8)R)³

= (4/3)π(0.512)R³

आयतन घटा = (4/3)πR³ - (4/3)π(0.512)R³

= (4/3)πR³ (1 - 0.512)

=  (4/3)πR³ (0.488)

आयतन % घटा =  {((4/3)πR³ (0.488) )/((4/3)πR³) } * 100

= 48.8 %