Question

Pyramid A is a square pyramid with a base side length of 18 inches and a height of 9 inches. Pyramid B has a volume of 3,136 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percentage. Provide an explanation and proof

Answer 1

@snowflake0531

Answer 2

hmm so there are a couple of steps we have to do.
1) find the area od the square at the borrom of the square pyramid \[ ( B=18 \times 18 ) \]

then use the formula to find the volume of the whole pyramid:
\[ V=\frac{B \times h}{3} \]
\[ B= \text{look above}\]
\[ h=9 \]
do the math, and after you find the volume of the pyamid sivide the volume of pyramid A with pyramid B:
\[ \frac{volume of pyramid A}{3.136} \]

Answer 3

972 inches ^3 is the volume of the pyramid

Answer 4

yes!

now do the 2nd part

Answer 5

309.948979592

Answer 6

lets round that to 309.95

so pyramid A, is 309.95 times bigger than pyamid b

how can we express that number as a percentage?

Answer 7

i dont know :(

Answer 8

we multiply that number by 100%

so:
\[ 309.95 \times 100\%=??\% \]

Answer 9

\[309\cancel{.95} \times 1 \cancel{00}\%=30995\%\]
so, pyramid A, is 30995% bigger than pyamid b.

Answer 10

\[volume~of~pyramid~A=\frac{ base~area \times height }{ 3 }=\frac{ 18\times 18\times 9 }{3 }\]
=972 inch ^3
volume of pyramid B=3,136 inch ^3
\[\frac{ volume ~of~pyramid~B }{ volume~of~pyramid~A}=\frac{ 3136 }{ 972 }\approx 3.2263374\]
\[volume~of~pyramid~B ~is ~322.63 \% more~than~volume~of~pyramid~A\]

Answer 11

wrong...

Answer 12

it is not 3.136
but it is 3,136 means 3136

Answer 13

I received a tag from this post but that reply was deleted.

I do agree with surjithayer's work.

You're supposed to divide

Volume B / Volume A

That's how you'll know how many times larger the second pyramid is from the first pyramid. And then you multiply by 100%

It is also 3,136 and not 3.136 as surjithayer already pointed out.

Answer 14

oh wow -- i somewhy had the idea of doing it the opposite way.