What is the scale factor of two similar pyramids with volumes of 8 ft^3and 343 ft^3?

Question

PLEASE ANSWER ASAP AND STATE HOW YOU FOUND IT!!! 

Answer 1

The scale factor of the volume of objects varies as the cube of the linear scale.

 

8 = 2³

343 = 7³

 

So the scale factor (linear) is 2/7.

Answer 2

Hi Jacklen,

   Assuming the pyramids are square with side s and slant height h the volume is v=h*s²/3. You were given the ration of two pyramids and were told they were (geometrically) similar so s₁=k*s₂ and h₁=k*h₂ where k is called the scale factor.

So now we can write v₁=h₁*s₁/3 and v₂=h₂*s₂/3   If we now take the ratio of v₁ to v₂ we have v₁/v₂=k³ and since you know the ratio of the pyramids volume you can calculate the scale factor k which looks to be about 3.5.

 

Hope this is clear and helps

 

Jim