Answer:
Q = 12800 cm^3
Explanation:
We do not have enough information to directly calculate the volume of shape Q. However, we can use the information provided to find a relationship between the volumes of shape P and shape Q, and then use this relationship to solve for the volume of shape Q.
Let's start with the surface area and volume formulas for a sphere, since both shapes P and Q could be spheres (or parts of spheres):
Surface area of a sphere = 4πr^2
Volume of a sphere = (4/3)πr^3
We don't know the radius of either sphere, but we can still use these formulas to find a relationship between their volumes. Let's divide the surface area of shape Q by the surface area of shape P:
2880 / 720 = (4πr^2 for shape Q) / (4πr^2 for shape P)
Canceling out the 4πr^2 terms gives:
4 = (Volume of shape Q) / (Volume of shape P)
Simplifying, we can multiply both sides by the volume of shape P:
4 * Volume of shape P = Volume of shape Q
Now we can substitute in the volume of shape P that was given:
4 * 3200 = Volume of shape Q
Solving this equation gives:
Volume of shape Q = 12800 cm^3
Therefore, the volume of shape Q is 12800 cm^3.