Question

A right rectangular prism has base dimensions of 3 inches by 12 inches and a height of 5 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches and a height of 5 inches. Are the volumes the same?
A.
Yes, because the heights are equal and the cross-sectional areas at every level parallel to the bases are also equal.
B.
Yes, because the figures are congruent.
C.
No, because the cross-sectional areas are not the same.
D.
No, because only the bases have the same area, not every cross section at every level parallel to the bases.

Answer 1

volume = length x width x height
volume 1 = 3 x 12 x 5 = 180 in^3
volume 2 = 4 x 9 x 5 = 180 in^3

The volumes are the same

Answer 2

so it the answer would be b?

Answer 3

The volume are the same however they do not have the same shape 1 is more rectangular. I would say the answer is A.

Answer 4

would you like a better explanation

Answer 5

yes please

Answer 6

So we know that the height of both of the prisms is 5 and we know that the base of both prisms have different lengths

Answer 7

the dimensions of the first base is 3 by 12 so the base equals 36 in^2.
the dimensions of the second base is 4 by 9 so the base equals 36 in^2.

Answer 8

Also any cross-sentional area parallel to the base will have the same area as the base
making A true

Answer 9

Additionally, think about a square and a rectangle the square has the dimensions of 4 by 4 while the rectangles dimensions are 2 by 8. The areas are equal however to two shapes/figure are not congruent
this is why b cannot be true

Answer 10

would you still like more explanation
Also could you please give me a metal

Answer 11

no i understand now. thank you so much.

Answer 12

Thanks for the metal. Good luck with your studying.