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P and Q are two geometrically similar solid shapes.

The total surface area of shape P is 720 cm squared
The total surface area of shape Q is 2880 cm squared

The volume of shape P is 3200 cm cubed

Calculate the volume of shape Q?

User Javierfdr
by
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1 Answer

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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.

User Carlota
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