High School

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You are painting the prize pedestals shown (including the bottoms). You need 0.5 pint of paint to paint the red pedestal.

The side lengths of the green pedestal are one-half the side lengths of the red pedestal. How much paint do you need to paint the green pedestal?

Answer :

Final answer:

To paint the green pedestal, you would need 0.0625 pints of paint, as the green pedestal's surface area is ¹⁄₈ of the red pedestal's.

Explanation:

To determine how much paint is needed for the green pedestal, we need to understand the relationship between the volume (or the amount of paint needed) and the dimensions of the pedestals. The amount of paint required is directly proportional to the surface area of the object being painted. Since the green pedestal has dimensions that are one-half the side lengths of the red pedestal, we can conclude that each dimension of the green pedestal is reduced by a factor of ½. Therefore, the surface area of the green pedestal, which dictates the amount of paint needed, would be ½2 (or ¼) of the surface area of the red pedestal for each face. However, since a cube has 6 faces, we need to consider the total surface area which would be ¼6 or ⅕3 (½ * ½ * ½ = ¹⁄₈) of the red pedestal's surface area. Given that the red pedestal requires 0.5 pint of paint, the green pedestal would need ¹⁄₈ of that amount.

So, the calculation for the paint needed for the green pedestal would be:

0.5 pints * ¹⁄₈ = 0.0625 pints

Therefore, you would need 0.0625 pints of paint to paint the green pedestal.

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