The volume of the rectangular prism is 10 cubic feet more than the volume of the right triangular prism. Find the volume of each figure.

Question

asked Mar 11, 2020 94.6k views

1 Answer

Andy Song · Answer 1 · 2020-03-17T22:32:15+0000

Answer:

The volume of the rectangular prism is
$45\ ft^3$

The volume of the triangular prism is
$35\ ft^3$

Explanation:

step 1

Find the volume of the rectangular prism

The volume of rectangular prism is equal to

V=x(6)(3)

$Vrp=18x\ ft^3$

step 2

Find the volume of the triangular prism

The volume of triangular prism is equal to

V=(1)/(2) (4)(x)(7)

$Vtp=14x\ ft^3$

step 3

we know that

The volume of the rectangular prism is 10 cubic feet more than the volume of the right triangular prism

Vrp=Vtp+10

substitute the given values and solve for x

18x=14x+10

18x-14x=10

4x=10

x=2.5

therefore

The volume of the rectangular prism is

$Vrp=18x\ ft^3$ ----->
$Vrp=18(2.5)=45\ ft^3$

The volume of the triangular prism is

$Vtp=14x\ ft^3$ ----->
$Vtp=14(2.5)=35\ ft^3$