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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.

The volume of the rectangular prism is 10 cubic feet more than the volume of the right-example-1

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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

User Andy Song
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