the world's largest cube puzzle in Knoxville measures 6 feet on each side. The scale factor between a standard cube puzzle and largest is 1/24. Find the surface area and volume of the standard cube puzzle.
Answer is 0.375ft^2/0.015625ft^3
Not sure how they figured it out
i thought it was 6 (6)^2 equals 216ft for the large cube divided by 1/24 but I don't get the right answer
nevermind, forgot to square it, figured it out
To find the surface area and volume of the standard cube puzzle, we need to use the scale factor provided and apply it to the measurements of the largest cube puzzle.
The scale factor is given as 1/24, which means that each side of the standard cube puzzle is 1/24th the length of each side of the largest cube puzzle.
Let's start by finding the length of each side of the standard cube puzzle. We will simply divide the length of each side of the largest cube puzzle by the scale factor:
Length of standard cube puzzle = Length of largest cube puzzle / Scale factor
Length of standard cube puzzle = 6 feet / 1/24
To divide by a fraction, we need to multiply by its reciprocal (flip the fraction):
Length of standard cube puzzle = 6 feet * (24/1)
Length of standard cube puzzle = 144 feet
Now that we have the length, we can calculate the surface area and volume of the standard cube puzzle.
Surface Area:
The surface area of a cube can be calculated using the formula: 6 * (side length)^2
Surface area of standard cube puzzle = 6 * (144 feet)^2
Surface area of standard cube puzzle = 6 * 20736 square feet
Surface area of standard cube puzzle = 124,416 square feet
Volume:
The volume of a cube can be calculated using the formula: (side length)^3
Volume of standard cube puzzle = (144 feet)^3
Volume of standard cube puzzle = 2985984 cubic feet
Therefore, the surface area of the standard cube puzzle is 124,416 square feet and the volume is 2,985,984 cubic feet.