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?

Answers

Answer 1

Answer:

Answer: 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

$a+b+c=518~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\n\na=(1)/(3)b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\n\nb=c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

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

$a+b+c=518\n\n\n\Rightarrow (1)/(3)b+b+b=518\n\n\n\Rightarrow (1)/(3)b+2b=518\n\n\n\Rightarrow (b+6b)/(3)=518\n\n\n\Rightarrow 7b=1554\n\n\n\Rightarrow b=(1554)/(7)\n\n\n\Rightarrow b=222.$

From equation (iii), we get

$b=c=222,$

and from equation (ii), we get

$a=(1)/(3)*222\n\n\n\Rightarrow a=74.$

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 2

Answer:

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 $(1)/(3)$ 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 $\boxed{ \ 1 \ unit = (518)/(7) \ cubic \ feet \ }$

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: $3 \ unit = 3 * 74 = \boxed{ \ 222 \ cubic \ feet \ }$

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

Learn more

Volume of rectangular prism brainly.com/question/11613210
What is the side length of each cube? brainly.com/question/6752459
Find out the area of a cube brainly.com/question/12613605#

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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Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

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