Answer:
8 times larger.
Step-by-step explanation:
The radius of the large sphere is double the radius of the small sphere.
Question asked:
How many times does the volume of the large sphere than the small sphere
Solution:
Let radius of the small sphere = [tex]x[/tex]
As the radius of the large sphere is double the radius of the small sphere:
Then, radius of the large sphere = [tex]2x[/tex]
To find that how many times is the volume of the large sphere than the small sphere, we will divide the volume of large sphere by volume of small sphere:-
For smaller sphere: [tex]Radius = x[/tex]
[tex]Volume \ of \ sphere = \frac{4}{3} \pi r^{3}[/tex]
[tex]=\frac{4}{3} \pi x^{3}[/tex]
For larger sphere: [tex]Radius = 2x[/tex]
[tex]Volume \ of \ sphere = \frac{4}{3} \pi r^{3}[/tex]
[tex]=\frac{4}{3} \pi (2x)^{3}[/tex]
Now, we will divide volume of the larger by the smaller one:
[tex]=\frac{4}{3} \pi (2x)^{3}\div\frac{4}{3} \times\frac{\pi }{1 } \times x^{3}\\ \\ =\frac{4}{3} \pi\times8x^{3} \times\frac{3}{4\pi }\ \times\frac{1}{x^{3} }[/tex]
[tex]\frac{4}{3}\pi\ is \ canceled\ by\ \frac{3}{4\pi } \ and\ also\ x^{3} is\ canceled\ by \ \frac{1}{x^{3} }[/tex]
Now, we have
= [tex]\frac{8}{1}[/tex]
Therefore, the volume of the large sphere is 8 times larger than the smaller sphere.
