We are given that the world's largest cube puzzle measures 6 feet on each side.
We want to find the surface area and volume of the standard cube puzzle. Let's start by finding the volume and surface area of the largest puzzle. Recall that the surface area and volume of a cube with side length s can be calculated using the following formulas.
S.A. & = 6 s^2 [0.3em]
V & = s^3In this case, s = 6. We can substitute this value into the formulas to calculate the surface area and volume of the largest puzzle. We will start with the surface area.
Therefore, the surface area of the largest puzzle is 216 square feet and the volume is 216 cubic feet. Now we will find the surface area and volume of the standard puzzle. To do so, recall the relationships between the surface areas and the volumes of similar solids.
Surface Area of Similar Solids
If Solid X is similar to Solid Y by a scale factor, then the surface area of X is equal to the surface area of Y times the square of the scale factor.
Volume of Similar Solids
If Solid X is similar to Solid Y by a scale factor, then the volume of X is equal to the volume of Y times the cube of the scale factor.
We are given that the scale factor between the two puzzles is 124. Note that the scale factor is less than 1. This means that the dimensions of the standard puzzle are smaller by a scale factor of 124 than the dimensions of the largest puzzle. Therefore, we can calculate the surface area and volume of the standard puzzle using the scale factor of 124. Let's do it!
Object
Surface Area, in^2
Volume, in^3
the world's largest cube puzzle
216
216
standard cube puzzle
216 (1/24)^2 = 0.375
216 (1/24)^3 = 0.015625
Therefore, the surface area of the standard cube puzzle is 0.375 square feet and the volume is 0.015625 cubic feet.
