Question

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.
The volume of pyramid A is___ the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B____ is the volume of pyramid A.

Answer 1

options are
half,equal to,twice,3 times

Answer 2

so.. hmm how do you get the volume of a pyramid anyway?

Answer 3

v=(lwh)/3

Answer 4

but that still doesnt give me an answer

Answer 5

notice.. their height "h" is the same

so... that means then
\(\textit{volume of A}=\cfrac{lwh}{3}\quad
\begin{cases}
w=20\\
l=10
\end{cases}\implies \cfrac{10\cdot 20\cdot h}{3}
\\ \quad \\
\textit{volume of B}=\cfrac{lwh}{3}\quad
\begin{cases}
w=10\\
l=10
\end{cases}\implies \cfrac{10\cdot 10\cdot h}{3}\)

so... how big is the volume of A to B then?

Answer 6

im not sure how to figure that out without h

Answer 7

can you explain?

Answer 8

well... notice.. 20* 10 = 200
and 10*10 = 100

thus \(\begin{cases}
A&\cfrac{200h}{3}\implies \cfrac{2\cdot 100h}{3}\implies 2{\color{brown}{\cfrac{100h}{3} }}\\
B&{\color{brown}{ \cfrac{100h}{3} }}
\end{cases}\)

so... how big is A's volume then?

Answer 9

66.66?

Answer 10

66.66? what?

Answer 11

66.66pi??

Answer 12

\(2{\color{brown}{\cfrac{100h}{3} }}\implies twice \cfrac{100h}{3}\)

notice the 2 in front

Answer 13

english is not my first language ,thats why its a little hard to understand word problems

Answer 14

so the first answer is twice and the second is 3 times

Answer 15

3 times? hmmm well
for the second part, you're asked to increase the height to twice as big as A's
though, notice A's height is the same as B's height
so, if you were to make B's height twice as A's, you're really just doubling it

because B's height is "h"
and A's heiight is also "h"
and twice the height of A is really 2*h = 2h
so, B's height will now be 2h then

so.. what would be the new volume for B using that as the height?

Answer 16

B's old height was (100h)/3 using just "h"
now that it becomes 2h, what would be the new height of B?

Answer 17

the new volume rather, of B

Answer 18

so it would be equal too