Respuesta :
Question is Incomplete; Complete question is given below;
3 rectangular prisms have a combined volume of 518 cubic feet. Prism A has 1/3 the volume of Prism B. Prisms B and C have equal volume.What is the volume. What is the volume of each prism.
Answer:
Volume of prism A is [tex]74\ ft^3[/tex] and Volume of Prism B and Volume of Prism C is [tex]222\ ft^3[/tex].
Step-by-step explanation:
Let the Volume of 3 prism be A,B,C.
Now Given:
3 rectangular prisms have a combined volume of 518 cubic feet.
so we can say that;
[tex]A+B+C=518 \ ft^3 \ \ \ \ equation \ 1[/tex]
Also Given:
Prisms B and C have equal volume.
[tex]B = C[/tex]
Also given:
Prism A has 1/3 the volume of Prism B.
so we can say that;
[tex]A=\frac{B}{3} = \frac{C}{3}\\\\B=C=3A[/tex]
Now Substituting the value of B and C in equation 1 we get;
[tex]A+B+C=518\\\\A+3A+3A=518\\\\7A=518[/tex]
Dividing both side by 7 we get;
[tex]\frac{7A}{7}=\frac{518}{7}\\\\A= 74 \ ft^3[/tex]
Now Substituting the value of A to find B and C we get;
[tex]B=C=3A=3\times74=222\ ft^3[/tex]
Hence Volume of prism A is [tex]74\ ft^3[/tex] and Volume of Prism B and Volume of Prism C is [tex]222\ ft^3[/tex].
