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.

answered: 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

answered: Guest

b, i believe, but not sure.

Can somebody me figure out the probability?

answered: Guest

you estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82 .the total height of the building is another 123 meters above the 86th floor.

leave feedback if u need : )

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Three rectangular prisms have a combined volume of 518 cubic feet. prism a has one-third the volume...