Question

if the radius of a sphere is tripled then what is the ratio of the volume of original sphere to that of the second.​

Answer 1

Answer:

1:9

Step-by-step explanation:

for 1st sphere

v1=1/3*πr³

for 2nd sphere

v2=1/3*π(3r³)

v1:v2=1/3*πr³:1/3*π(3r)³

=r³:(3r)³

=1:9

Answer 2

Ratio of Volume of original sphere to the second sphere is 1 : 27.

Step-by-step explanation:

Step 1 - Volume of First or original sphere

Radius of sphere = r

Volume of sphere = V = $\frac{4}{3}$ × π × $r^{3}$

Step 2 - Volume of second sphere

Radius of second sphere = 3r

Volume of second sphere = V' = $\frac{4}{3}$ × π × $(3r)^{3}$

                                          =   $\frac{4}{3}$ × π × 27 $r^{3}$

Step 3 - Ratio of Volume of first sphere to the second sphere

    $\frac{V}{V'}$  =  $\frac{ \frac{4*\pi*r^{3} }{3} }{ \frac{4 * \pi*27 * r^{3} }{3} }$   =  $\frac{1}{27}$

and the ratio of V : V' = 1 : 27.