SOLUTION: A rectangular piece of cardboard with perimeter 30 in., two parallel and equally spaced creases are made. The cardboard is then folded to make a prism with open ends that are equil
Algebra.Com
Question 164928: A rectangular piece of cardboard with perimeter 30 in., two parallel and equally spaced creases are made. The cardboard is then folded to make a prism with open ends that are equilateral triangles. Find the volume of the prism as a function of x and what is the domain of V(x)? Thanks to those who can help!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular piece of cardboard with perimeter 30 in., two parallel and equally spaced creases are made. The cardboard is then folded to make a prism with open ends that are equilateral triangles. Find the volume of the prism as a function of x and what is the domain of V(x)?
:
Let x = the 3 equal distances, between the two folds
then
3x = width of the cardboard
and
Let L = the length of cardboard
;
Perimeter:
2(3x) + 2L = 30
Simplify divide by 2
3x + L = 15
L = (15-3x)
:
Find the height (h) of the equilateral triangle with sides = x
h^2 + (x/2)^2 = x^2
h^2 = x^2 - (x/2)^2
h =
:
Vol of a triangular prism = *L*w*h
In this problems
L = (15-3x)
w = x
h =
:
V(x) = *(15-3x)*x*
:
You can tell by L, (15-3x), that x has to be less than 5 (the domain)
:
If you graph this:
The max volume when x = 3.33, Domain 0 to <+5
RELATED QUESTIONS
On a rectangular piece of cardboard with perimeter 14 inches, three parallel and equally... (answered by josmiceli)
On a rectangular piece of cardboard with perimeter 10 inches, three parallel and equally... (answered by ankor@dixie-net.com)
On a rectangular piece of cardboard with perimeter 13 inches, three parallel and equally... (answered by ikleyn)
A rectangular piece of cardboard measures 18 cm by 15 cm. What is the perimeter of the... (answered by rfer)
APPLIED PROBLEMS ( need equation and solution)
A rectangular cardboard is to be made... (answered by josgarithmetic,mananth)
(APPLIED PROBLEM) What is the equation and solution:
A rectangular cardboard is to be... (answered by ankor@dixie-net.com)
A box with an open top is made from a rectangular piece of cardboard by cutting a square... (answered by stanbon)
An open box is formed from a rectangular piece of cardboard, whose length is 3 inches... (answered by texttutoring)
Use quadratic formula and a calculator to solve. Round decimal approximations to the... (answered by josgarithmetic)