Nova Physics Question from Ch1

[klonchy]

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Hello SDN community,

I have just begun studying for the physics portion of the MCAT and I am using Nova's MCAT Physics book.

I came across a relatively simple problem (but a problem nonetheless) which I want to run by you all:
Page 8 Question 19
Given the formula for the volume of a pyramid with a square bas:
V = (1/3) s^2 h
s = length of a side, h = perpendicular height

If every linear dimension of a square pyramid were increased by a factor of 3, how would the volume change?
a increase by a factor of 3
b increase by a factor of 9
c increase by a factor of 27
d increase by a factor of 81

The text says that the answer is C. But this does not take into account the (1/3) in the problem. Why would the answer not be B? Any thoughts?

Thanks in advance for your help.

 

[kehlsh]

V = (1/3) s^2 h

let's say s = 1, h = 1

v = 1/3

let's say s = 3, h = 3

v = 3

1/3 stays constant... in other words, it's included in both before and after so it doesn't affect the change in volume

 

[klonchy]

V = (1/3) s^2 h

let's say s = 1, h = 1

v = 1/3

let's say s = 3, h = 3

v = 3

1/3 stays constant... in other words, it's included in both before and after so it doesn't affect the change in volume

kehlsh thank you for your response. This is how I approached the problem initially.
when s=1 & h=1, v = (1/3)(1)^2(1) = (1/3)
when both linear dimensions are triplicated (s & h)
v = (1/3)(3)^2(3) = 9 (you wrote 3 but I think you meant 9)

I guess the takeaway from your message is that since the (1/3) exists in both scenarios...treat them as constants and omit; by doing this I would get the correct answer....

 

[kehlsh]

kehlsh thank you for your response. This is how I approached the problem initially.
when s=1 & h=1, v = (1/3)(1)^2(1) = (1/3)
when both linear dimensions are triplicated (s & h)
v = (1/3)(3)^2(3) = 9 (you wrote 3 but I think you meant 9)

I guess the takeaway from your message is that since the (1/3) exists in both scenarios...treat them as constants and omit; by doing this I would get the correct answer....

yea i meant 9 haha