In this lesson, we will learn how to find the ratio between the surface area and volume of different shapes.

Q1:

Consider a sphere that initially has a radius 𝑟.

If 𝑟 changes by a factor of 3, by what factor does the volume of the sphere change?

By what factor does the surface area of the sphere change?

Q2:

Consider a cube that initially has side length 𝑥.

If 𝑥 increases by a factor of two, by what factor does the volume of the cube change?

By what factor does the surface area of the cube change?

Q3:

Consider a cube of side length 𝑥.

Which of the following is the correct equation for the volume, 𝑉, of the cube?

Which of the following is the correct equation for the surface area, 𝐴, of the cube?

Which of the following is the correct equation for the ratio of the volume of the cube to its surface area?

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