Question

a spherical balloon grows to twice its radius when inflated how has its volume increased

Answer 1

Let radius of uninflated balloon is x.
=> V=4/3 pie r³
=>V' volume of inflated balloon =4/3pie(2r)³
=>V'/v=4/3pie×8r³/4/3pie r³
=>V'/V =8/1
=>V'=8V

Answer 2

A spherical balloon grows to twice its radius then inflated Volume will be equal to 8 times the Volume.

Step-by-step explanation:

Given:

a spherical balloon grows to twice its radius when inflated.

Now let the radius of uninflated Spherical balloon be 'r'.

So According to question radius of inflated Spherical balloon = $2r$

Now we know that balloon is in spherical form.

So Volume of Sphere is given by 4/3 times π times cube of the radius.

framing in equation form we get;

Now Volume of uninflated balloon $V_1=\frac{4}{3}\pi r^3$

So Volume of Inflated balloon $V_2=\frac{4}{3}\pi (2r)^3 = \frac{4}{3}\pi 8r^3$

Now We will Divide Volume of Inflated balloon with Volume of uninflated balloon.

$\frac{V_2}{V_1}=\frac{\frac{4}{3}\pi 8r^3}{\frac{4}{3}\pi r^3}\\\\\frac{V_2}{V_1} = \frac{8}{1}\\\\V_2=8V_1$

Hence we can say that a spherical balloon grows to twice its radius then inflated Volume will 8 times the Volume.