Help,help headache please

[Kimiko]

Question.... How many times greater is the volume of the actual pyramid than the volume of the model? The pyramid has a square base that is 214.5m on each side, a height of 143.5m, and a slant height of 179.4m. Scale is 6m/2cm sq.

I did get the total surface area of 13,663.7 cm sq but am having problems with volume.

V=1/3 Bh
V=1/3 {1/2 (214.5) (179.4) h}
V=1/3 (1/2 ^214.5 ^214.5) 179.4
V=1361950.9 cubic cm

scale ratio 6m=2cm sq 6 sq m = 2 sq cm
scale ratio 6m=2cm cu 216 cubic m = 8 cubic cm

1361950.9 meter sq = x cm sq
x= 8(1361950.9) divided by 36 = 10895607 divided by 216=50442.625
difference is 1361950.9 - 50442.625= 1311508.3 cubic meter HELP HELP

 

[birdie_boo]

Math Sence

OK. When there is a slant DON'T use it! There is usually a dotted line that runs through the middle that tells you the height. If that helps anybody...!

 

[Kimiko]

Formula

Kimiko, the volume of a square pyramid = b^2 * h / 3 ; where did you get bh/3?
So in your case: 214.5^2 * 143.5 / 3 = ~2,200,824
Slant height not required.

Note: ^2 means to the power 2 (or squared); 4^2 = 16

This was the formula in the text for volume of pyramid. V=1/3Bh
So, my answer with your formula is 2200826cm (squared)

Now to figure out how many times the actual volume is greater than the volume of the model, I need to convert to cm then ratio?
EX 214.5^2 *2cm)( 143.5*2cm) then (214.5^2*6m)(143.5*6m) Scale is 6m to 2 cm
Ex Ratio: 6*100=600cm
Multiple Choice Answers are: 27 times, 300 times, 27,000,000 times and 9,000,000 times.

Denis, Thank you so much for the assistance. I really do appreciate your explanation.

 

[Deleted member 4993]

This was the formula in the text for volume of pyramid. V=1/3Bh
So, my answer with your formula is 2200826cm (squared)

Something wrong here .... volume CANNOT have a dimension of cm²

Check your work carefully....

Now to figure out how many times the actual volume is greater than the volume of the model, I need to convert to cm then ratio?
EX 214.5^2 *2cm)( 143.5*2cm) then (214.5^2*6m)(143.5*6m) Scale is 6m to 2 cm
Ex Ratio: 6*100=600cm
Multiple Choice Answers are: 27 times, 300 times, 27,000,000 times and 9,000,000 times.

Denis, Thank you so much for the assistance. I really do appreciate your explanation.

.

 

[Mrspi]

I am unable to follow what the original poster has shown....

I DO have a hint, however.

If two figures are similar, then the ratio of the volumes is the CUBE of the ratio of any two corresponding lengths.

Say, for example, the ratio of the lengths of a side of the square base is 10/3. Then, the ratio of the volumes of the two solids would be (10/3)³, or 1000/27.

That would mean that the volume of the larger figure is (1000/27) times the volume of the smaller figure.

If, among your indecipherable (to me, anyway) information you have a pair of corresponding lengths, find the ratio of those lengths (making sure the lengths are given in terms of the same UNIT, like meters and meters, or cm and cm) and cube that ratio. That will tell you how the volumes compare.