Respuesta :
If the radius of sphere is tripled, then volume does not triple. But volume increases by a factor of 27
Solution:
Given if the radius of sphere is tripled, whether the volume of sphere triples or not
The volume of sphere is given as:
[tex]v = \frac{4}{3} \pi r^3[/tex]
Where "r" is the radius of sphere
When radius is tripled:
r = 3r
Let [tex]v_1[/tex] be the volume when radius is tripled
[tex]v_1 = \frac{4}{3} \pi (3r)^3\\\\v_1 = \frac{4}{3} \pi \times 27 \times r^3\\\\v_1 = 27(\frac{4}{3} \pi r^3)[/tex]
[tex]v_1 = 27 v[/tex]
volume when radius is tripled = 27 times volume of sphere when radius is "r"
Therefore, if the radius is tripled the volume increases by a factor of 27
So the volume does not gets tripled
