Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
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
[tex]a+b+c=518~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\a=\dfrac{1}{3}b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\b=c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the values of a and c from equations (ii) and (iii) in equation (i), we get
[tex]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.[/tex]
From equation (iii), we get
[tex]b=c=222,[/tex]
and from equation (ii), we get
[tex]a=\dfrac{1}{3}\times222\\\\\\\Rightarrow a=74.[/tex]
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.
- 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 [tex]\frac{1}{3}[/tex] 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.
[tex]Prism B: \boxed{\circ}\boxed{\circ}\boxed{\circ}[/tex]
[tex]Prism C: \boxed{\circ}\boxed{\circ}\boxed{\circ}[/tex]
[tex]Prism A: \boxed{\circ}[/tex] 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.
[tex]\boxed{ \ 7 \ unit = 518 \ cubic \ feet \ }[/tex]
[tex]\boxed{ \ 1 \ unit = ? \ cubic \ feet \ }[/tex]
Then [tex]\boxed{ \ 1 \ unit = \frac{518}{7} \ cubic \ feet \ }[/tex]
Hence, [tex]\boxed{\boxed{ \ 1 \ unit = 74 \ cubic \ feet \ }}[/tex]
And now, let us calculate the volume of each prism.
The volume of Prism A: [tex]1 \ unit = \boxed{ \ 74 \ cubic \ feet \ }[/tex]
The volume of Prism B: [tex]3 \ unit = 3 \times 74 = \boxed{ \ 222 \ cubic \ feet \ }[/tex]
The volume of Prism C: [tex]3 \ unit = 3 \times 74 = \boxed{ \ 222 \ cubic \ feet \ }[/tex]
Learn more
- Volume of rectangular prism https://brainly.com/question/11613210
- What is the side length of each cube? https://brainly.com/question/6752459
- Find out the area of a cube https://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
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
