Question

How many times larger is the volume of a sphere if radius is multiplied by 5

Answer 1

Answer:

Given:

• to find volume of a sphere if radius is multiplied by 5

Formulas :

• Volume of sphere = $\dfrac{4}{3}\pi r^3$

Solving Question:

  We have consider 'r' as the radius and find the volume then in second  case  '5r' as the new radius and find its volume .Therefore we can find the answer

⇒ 'r' as the radius in first case

⇒ '5r' as radius in second case

Solution:

   First case ; 'r' as the radius

volume = $\dfrac{4}{3}\pi r^3\\\\substitute\:values\\\\\implies \dfrac{4*\pi*r^3}{3}$

Second case ; '5r' as radius

volume = $\dfrac{4*\pi*(5r)^3}{3}$

To find how many times larger =$\dfrac{Volume\:in\:second\:case}{Volume\:in\:first\:case}$

⇒$\huge{\dfrac{\dfrac{4*\pi*(5r)^3}{3}}{\dfrac{4*\pi*r^3}{3}}}\\\\\implies \dfrac{(5)^3}{1}\\\\\implies 125$

Thus it will be 125 times larger