Respuesta :
Answer : The ratio of the volume of Sphere A to the volume of Sphere B is, 64 : 27
Step-by-step explanation :
Formula used to calculate the volume of sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
First we have to calculate the volume of sphere A.
Given:
r = radius of sphere A = 4 inch
[tex]V_A=\frac{4}{3}\pi (4)^3[/tex]
[tex]V_A=\frac{256}{3}\pi \text{ inch}^3[/tex]
Now we have to calculate the volume of sphere B.
Given:
r = radius of sphere B = 3 inch
[tex]V_B=\frac{4}{3}\pi (3)^3[/tex]
[tex]V_B=36\pi \text{ inch}^3[/tex]
Now we have to calculate the ratio of the volume of Sphere A to the volume of Sphere B.
[tex]\frac{V_A}{V_B}=\frac{\frac{256}{3}\pi \text{ inch}^3}{36\pi \text{ inch}^3}[/tex]
[tex]\frac{V_A}{V_B}=\frac{64}{27}[/tex]
Therefore, the ratio of the volume of Sphere A to the volume of Sphere B is, 64 : 27
