Two pyramids are similar with a ratio of surface areas of 25:64, Find the volume of the second pyramid given the first has a volume of 250m^3.
thanks in advance.
2007-06-20 03:07:11 · 8 answers · asked by tochau 5 in Science & Mathematics ➔ Mathematics
ania: when I did it your way i got 16....and i dont think that's it.
doctor Q: i've never done it your way before
2007-06-20 03:16:36 · update #1
Remember:
ratio of one-dimension (length for example) is a:b
ratio of two-dimensions (surface area) is a^2 : b^2
ratio of three-dimensions (volume) is a^3 : b^3
================
Surface Areas = 25 : 64
Take the square root to get the ratio of the lengths:
5 : 8
Cube that to get the ratio of the volumes:
125 : 512
125 / 512 = 250 / x
125x = 250(512)
x = (250)(512) / 125 = 1024 m^3
2007-06-20 03:14:16 · answer #1 · answered by Mathematica 7 · 0⤊ 0⤋
I'm not sure what "m" is, although I'm assuming you want your final answer with an "m" in it.
Here's the way to set up the problem:
(volume of first pyramid / volume of second pyramid) = 25 / 64
Now use some variable for the volume of the second pyramid (I'll use V) and you get the equation:
250m^3 = 25
----------- ----
V = 64
Cross-multiplying gives:
(250m^3) * 64 = 25 * V
Now solve for V
(250m^3 * 64) / 25 = V
250 / 25 * 64 * m^3 = V
10 * 64 * m^3 = V
640m^3 = V
So the volume of the second pyramid is 640m^3
2007-06-20 10:17:55 · answer #2 · answered by grompfet 5 · 0⤊ 0⤋
Ratio of areas = 25:64
Ratio of lengths = 5:8
Ratio of volumes = 125 : 512
Volume of 2nd pyramid = 250 x (512 / 125) m³
= 1024 m³
2007-06-20 11:02:43 · answer #3 · answered by Como 7 · 0⤊ 0⤋
surface area of pyramid A : surface area of pyramid B
25 : 64
volume of pyramid A : volume of pyramid B
25 * height : 64 * height
250 m³ : x m³
x/64 = 250/25
x = (64 * 250)/25 = 640 m³
volume of second pyramid: 640 m³
2007-06-20 10:15:01 · answer #4 · answered by jurassicko 4 · 0⤊ 0⤋
To do this you need to find the scale factor, a:b, by square rooting the surface areas. It is 5:8.
Then you set up a proportion a^3:b^3=Volume1/Volume 2
Cross multiply and solve.
2007-06-20 10:12:44 · answer #5 · answered by ania 2 · 1⤊ 0⤋
First we take the ratio-: 25:64
64 / 25 = 2.56
Now we cube this amount to allow for the change in area in the three axis (x,y,z)
2.56^3 = 16.777216
Now we multiply the 1st surface area by this....
250 x 16.777216 = 4194.304 m^3
NOTE!!! Now I've seen Mathmatica's way, I think he's got it correct.
2007-06-20 10:12:33 · answer #6 · answered by Doctor Q 6 · 0⤊ 1⤋
specify the base of the pyramid; square or hexagonal or what?
2007-06-20 10:14:16 · answer #7 · answered by psbhowmick 6 · 0⤊ 0⤋
wow can some one anwser what grade this is?
and i also love how all 3 answers are all different lol.
2007-06-20 10:15:26 · answer #8 · answered by Anonymous · 0⤊ 0⤋