MULTIPLE CHOICE SCALE FACTOR?
A gift shop in Cairo sells a tiny pyramid pendant. Due to its popularity, the shop decided to make a larger, yet similar version, that was double the volume of the original.
Determine the scale factor relating the dimensions of the two pyramids.
A. K = 2
B. K = 8
C. K = square root of 2
D. K = ^3square root of 2
What is the factor relating the surface area of the original pendant to the new larger pendant?
A. ^6square root of 2
B. ^3square root of 4
- davidLv 71 month ago
V = (1/3)Bh === B = 1^2 = 1
V = (1/3)h ... h = (sqrt6)/2
New V = (1/3)Bh ... B = s^2 ... h = s(sqrt6)/2
2 = (1/3)(s^2)s(sqrt6)/2
12/(sqrt6) = s^3
s = cuberoot[12/(sqrt6)] <<< scale factor
rationalize if you want (or need to)
- PuzzlingLv 71 month ago
Note: ^3square and ^6square don't make much sense. I think you are trying to say the cube root and the 6th root.
When you scale a shape up proportionally, you have the following:
All linear (1D) measurements have a scale factor of k.
All area (2D) measurements have a scale factor of k².
All volume (3D) measurements have a scale factor of k³.
You are told that your volume scales by 2 (double), so:
k³ = 2
To figure out the scale factor (k) for all the linear measurements, take the cube root of both sides:
k = ∛2
For the second part, you are talking about areas, so the scale factor for areas is k²
k² = (∛2)² = ∛2 * ∛2 = ∛(2*2) = ∛4