Mathematics, 18.08.2019 16:00 Tdhaynes7759

Three rectangular prisms have a combined volume of 518 cubic feet. prism a has one-third the volume of prism b, and prisms b and c have equal volume. what is the volume of each prism?

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The volume of Prism A is 74 cubic feet, volume of Prism B is 222 cubic feet and the volume of Prism C is 222 cubic feet.

Step-by-step explanation: Given that three rectangular prisms have a combined volume of 518 cubic feet. Prism A has one-third the volume of Prism B and Prisms B and C have equal volume.

We are to find the volume of each of the three prisms.

Let, a, b and c represent the volumes of Prism A, Prism B and Prism C respectively.

The, according to the given information, we have

$a+b+c=518~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\a=\dfrac{1}{3}b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\b=c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the values of a and c from equations (ii) and (iii) in equation (i), we get

$a+b+c=518\\\\\\\Rightarrow \dfrac{1}{3}b+b+b=518\\\\\\\Rightarrow \dfrac{1}{3}b+2b=518\\\\\\\Rightarrow \dfrac{b+6b}{3}=518\\\\\\\Rightarrow 7b=1554\\\\\\\Rightarrow b=\dfrac{1554}{7}\\\\\\\Rightarrow b=222.$

From equation (iii), we get

b=c=222,

and from equation (ii), we get

$a=\dfrac{1}{3}\times222\\\\\\\Rightarrow a=74.$

Thus, the volume of Prism A is 74 cubic feet, volume of Prism B is 222 cubic feet and the volume of Prism C is 222 cubic feet.

Answer from: jdbessix3567

The volume of Prism A is 74 cubic feet.The volume of Prism B is 222 cubic feet.The volume of Prism C is 222 cubic feet.Further explanation

Given:

Three rectangular prisms have a combined volume of 518 cubic feet.

Prism A has one-third the volume of Prism B, and Prisms B and C have equal volume.

Question:

What is the volume of each prism?

The Process:

Prism A has $\frac{1}{3}$ the volume of Prism B. From the denominator 3, let us draw a diagram representing the volume of Prisms B and C, then Prism A. Remember, both prisms have the same volume.

$Prism B: \boxed{\circ}\boxed{\circ}\boxed{\circ}$

$Prism C: \boxed{\circ}\boxed{\circ}\boxed{\circ}$

$Prism A: \boxed{\circ}$ or 1 of 3 units.

From all the diagrams above, it appears that the total units are 3 + 3 + 1 = 7 units.

Three rectangular prisms have a combined volume of 518 cubic feet. Therefore, we can calculate the volume of one unit diagram.

$\boxed{ \ 7 \ unit = 518 \ cubic \ feet \ }$

$\boxed{ \ 1 \ unit = ? \ cubic \ feet \ }$

Then $\boxed{ \ 1 \ unit = \frac{518}{7} \ cubic \ feet \ }$

Hence, $\boxed{\boxed{ \ 1 \ unit = 74 \ cubic \ feet \ }}$

And now, let us calculate the volume of each prism.

The volume of Prism A: $1 \ unit = \boxed{ \ 74 \ cubic \ feet \ }$

The volume of Prism B: $3 \ unit = 3 \times 74 = \boxed{ \ 222 \ cubic \ feet \ }$

The volume of Prism C: $3 \ unit = 3 \times 74 = \boxed{ \ 222 \ cubic \ feet \ }$

Learn moreVolume of rectangular prism What is the side length of each cube? Find out the area of a cube

Keywords: three rectangular prisms, have, a combined volume, 518 cubic feet, Prism A, has one-third, the volume, Prism B, C, equal, what, each prism, units, diagram

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