Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# 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

C. 4

D. 8 Relevance
• 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)

• 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