Precalculus Textbook 8th Edition Section 1.7 Exercise 33 Solution
Question:
A square of side x inches is cut out of each corner of a 10 in. by 18 in. piece of cardboard and the sides are folded up to form an open-topped box.
(a) Write the volume V of the box as a function of x.
(b) Find the domain of your function, taking into account the restrictions that the model imposes in x.
(c) Use your graphing calculator to determine the dimensions of the cut-out squares that will produce the box of maximum volume.
Online Precalculus Course |
One to One Student Class Fee: 20 USD Per Hour |
One to Five Student Class Fee: 15 USD Per Hour |
Batch 1 Timing (IST-Indian Standard Time): 3:00 AM to 4:00 AM |
Batch 2 Timing (IST-Indian Standard Time): 4:00 AM to 5:00 AM |
Batch 3 Timing (IST-Indian Standard Time): 5:00 AM to 6:00 AM |
Batch 4 Timing (IST-Indian Standard Time): 6:00 AM to 7:00 AM |
Batch 5 Timing (IST-Indian Standard Time): 7:00 AM to 8:00 AM |
Batch 6 Timing (IST-Indian Standard Time): 8:00 AM to 9:00 AM |
For More Details:Click Here to WhatsApp |
Solution:
Since the dimension of rectangular cardboard is 18 by 10,
If a square of x unit is cut from each of the vertex of the rectangular cardboard, then a rectangular box is made of the dimension l = (18 – 2x), b = (10 – 2x) and h = x.
Then, the volume of box is
V = lbh
= (18 – 2x)(10 – 2x)(x)
= 4x(x – 5)(x – 9)
= 4x(x2 – 14x + 45)
= 4x3 – 56x2 + 180x
(a) Function of Volume of the box is V = f(x) = 4x3 – 56x2 + 180x.
(b) Domain the function f(x) = 4x3 – 56x2 + 180x is x belongs to (0, 5).
(c) To get the maximum volume of the box, the value of x = 2.06
Precalculus Tutoring Online
For More details about the AP Precalculus Course Details, Click Here.
For more update about AMBIPi Tutors, Join WhatsApp Channel.