1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
larisa86 [58]
3 years ago
15

You are planning to make an open rectangular box from a 24​-in.-by-47​-in. piece of cardboard by cutting congruent squares from

the corners and folding up the sides. What are the dimensions of the box of largest volume you can make this​ way, and what is its​ volume?

Mathematics
1 answer:
miskamm [114]3 years ago
7 0

Answer:

The dimensions are  13.92inches by 36.92inches by 5.04inches

Volume is 2590.18 inches³

Step-by-step explanation:

see attachment for the figure

supposing 'h' is side length of the square and also the height of the box

then, According to the question

Length of the box 'L'= 47 - 2h

Width of the box 'w'= 24 - 2h

Volume of the box 'V'= hLw

Substituting the values of 'L' and 'w' in above equation

V= h(47 - 2h)(24 - 2h)

V=(47h - 2h²)(24 - 2h) => 1128h - 94h²-48h²+4h³

V= 4h³ -142h²+1128h -->eq(1)

Taking derivative on both sides.

V' = 12h² - 284h + 1128

Setting the equation to zero, we will have

0=12h² - 284h + 1128

0= 3h² - 71h + 282

Using Quadratic formula to find h

h=  (-b+-√b²-4ac) / 2a

  = 71+-√71² - (4 x 3 x 282) / (2 x 3)=> 71+-√5041- 3384 / 6

h  =(71+- 40.706)/ 6

EITHER h= 18.6

OR h=5.04

By substituting the value of 'h' in eq(1)

(1)=>V(18.6)= 4(18.6)³ -142(18.6)²+1128(18.6) => -2406.096

(1)=>V(5.04)= 4(5.04)³ -142(5.04)²+1128(5.04) => 2590.18

By ignoring the negative value, we will have h=5.04

Therefore,

L= 47 - 2h => 47 -2(5.04) =>36.92

w= 24 - 2h=> 24- 2(5.04)=> 13.92

The dimensions are  13.92inches x 36.92inches x 5.04inches

Volume is 2590.18 inches³

You might be interested in
The formula for the area A of a rectangle with length l and width w is A = l ⋅ w . Find A if: l = 23 feet and w = 15 feet The ar
dexar [7]

Answer:

345 sq. ft

Step-by-step explanation:

You know that the area is the length times the width. Simply plug in values to your equation:

A = l * w

A = 23 * 15

A = 345

The area is 345 square feet.

3 0
3 years ago
Evaluate x + y when x = - 18.2 and y = 3.6
Contact [7]
-18.2 + 3.6= -14.6 is the answer to the question
3 0
3 years ago
Read 2 more answers
A cone has a radius of 4 units and a height of 6 units.
zubka84 [21]

Answer:

Volume of the cone: 32π cubed unit

Step-by-step explanation:

Volume of cone: V=1/3hπr²

1/3 x 6 x π x 4^2 = 32π

7 0
3 years ago
Read 2 more answers
A student received a coupon for 17% off the total purchase price at a clothing store. Let c be the
lys-0071 [83]
C - 0.17c = 0.83c
When you write “c” at the start, or x or whatever, it has an understood (invisible) number 1. So you’re subtracting the decimal on the next variable from 1.
7 0
3 years ago
Select the correct solution set. 50 ≥ 15x
Semenov [28]
The answer (i think) is 3 <span>≥</span> x. hope i helped
7 0
3 years ago
Other questions:
  • Misha found that the equation -|2x-10|-1=2 had two possible solution x=3.5and x =-6.5. Which explains whether or not her solutio
    14·2 answers
  • 71, X
    5·1 answer
  • Can someone help me again pleaseeee :')
    15·1 answer
  • Unit Rates: One person walks 9/20 miles in each 3/4 hour. Another person walks 8/15 miles in each 2/3 hour. Who is faster?
    14·1 answer
  • Find the probability of rolling factors of 3
    10·1 answer
  • 12 1/2 as a decimal .......................................................
    10·2 answers
  • Suppose that a new fuel-efficient European car travels an average of 26 kilometers on 1 liter of gas. If gas costs 2.25 euros pe
    9·2 answers
  • A costume designer made 10 costumes that each used 5.8 yards of fabric. If she had 238.2 yards of fabric to start with, about ho
    8·1 answer
  • What is an equation of the line that passes through the points (-8, 2) and (-4, -3)?
    15·1 answer
  • 6 + (-9) - (-4) - 3 <br> help
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!