Question

MEDAL!!!!
17. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 24 cm, a width of 3 cm, and a height of 12 cm. The pyramid has a height of 21cm. Find the volume of the composite space figure.
A. 4,032cm^3
B. 2,376 cm ^3
C. 1,368 cm^3
D. 792cm^2

Answer 1

@dimensionx

Answer 2

do you know the formula for a pyramid..?

Answer 3

or the formula for the volume of a right prism..?

Answer 4

Draw it out and label it. That's always the first step.

Answer 5

no i don't know the formula..

Answer 6

ok i did that

Answer 7

Oh,I drew it wrong -_-

Answer 8

Oh no I didn't!!! omg, sorry.

Answer 9

oh... so what is the first step?

Answer 10

ok.. so the volume of a right prism

V = base area x height

so multiply length and width, then multiply the answer by the height of the prism

Answer 11

864?

Answer 12

the pyramid has a volume

V = 1/3 x base area x height

it has the same base area as the prism... so substitute that value

then multiply by the height of the pyramid and divide the answer by 3

last part... add the 2 volumes together.

Answer 13

wait so v=1/3x(24)x(12)

Answer 14

don't forget the units are cubed

so cm^3

the prism is correct...

for the pyramid the base area is 24 x 3

Answer 15

and the height is 21

Answer 16

ok so 24x3=72 and then 72x21=1,512

Answer 17

and you need to divide the answer for the pyramid by 3... ad the formula says

V = 1/3 x base area x height

then add the 2 volumes together

Answer 18

1512/3=504

Answer 19

that's correct... now just add the 2 volumes together

don't forget the units are cm^3

Answer 20

1368cm^3