Question

Pyramid A is a square pyramid with a base side length of 12 inches and a height of 8 inches. Pyramid B is a square pyramid with a base side length of 48 inches and a height of 32 inches. How many times bigger is the volume of pyramid B than pyramid A?

Answer 1

Volume of a square pyramid is \(a^2\large\frac{h}{3}\) where \(a\) is the base side length and \(h\) is the height of the pyramid.
Calculate the volume of both pyramids by the values given and get \(\frac{V_B}{V_A}\).

Answer 2

I don't understand @Sachintha

Answer 3

Let,
\(\large V_A=a_A^2\times\Large\frac{h_A}{3}\)
\(\large V_B=a_B^2\times\Large\frac{h_B}{3}\)

So to by \(\frac{V_B}{V_A}\) you can get how big is \(V_B\) relative to \(V_A\).

\(\Large \frac{V_B}{V_A}=\frac{a_A^2\LARGE\frac{h_A}{3}}{a_B^2\LARGE\frac{h_B}{3}}\)

\(\therefore\Large \frac{V_B}{V_A}=\frac{a_A^2h_A}{a_B^2h_B}\)

ex:
\(\large V_A=12^2\times\Large\frac{8}{3}=\normalsize 384\)

Answer 4

well a simple method that doesn't require finding values and then comparing is to recongise that the pyramids are similar...

the ratio of the measurements in pyramid A to pyramid B is 1:4

when comparing the volume of similar pyramids the ratio of the volumes is

\[1^3 : 4^3\]

this is because volume is a 3 dimensional measurement

if you where comparing surface areas the ratio would be

\[1^2 :4^2\]

this would be because area is a 2 dimension measurement

hope it helps and makes sense.

Answer 5

campbell's method is much easier. Didn't thought of it earlier. :3

Answer 6

Would the answer be 23,760 ? @Sachintha @campbell_st

Answer 7

I don't know what your answer represents...? can you tell me..?

Answer 8

How much bigger the volume of B it to A @campbell_st

Answer 9

if you are going to find the volumes

you need to take the larger volume and divide it by the smaller volume...

this will give you how many times larger....

or use the ratio of linear measures in similar solids to find the ratio of volumes

\[1^3 : 4^3\]

both methods will give the same answer

Answer 10

@amandathatgirl123321 Can you show me your working on how you plugged in those values to get your answer?

Answer 11

wow i was way off sorry guys.its 64 times bigger right ?

Answer 12

@Sachintha

Answer 13

Correct! @amandathatgirl123321 . campbell's method is much easier since you can get a ratio by any side and solve it to volume.
\(12:48\quad\Rightarrow\quad8:32\quad\Rightarrow\quad1:4\)
\(1^3:4^3\quad\rightarrow\quad1:64\)