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
labwork [276]
3 years ago
15

an open rectangular cardboard box with a square base is to have a volume of 256cm^3. Find the dimensions of the box if the area

of cardboard used is as small as possible
Mathematics
1 answer:
Anit [1.1K]3 years ago
5 0
Let
x------> the length side of the square base of the box
y-------> the height of the box

we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²-------->  equation 1

<span>The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.</span>

surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x

step 1 
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm

the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm

You might be interested in
Thirty work orders are selected from a filing cabinet containing 500 work order folders by choosing every 15th folder. which sam
Andru [333]
It is Systematic sampling
5 0
3 years ago
7th grade math help me pleaseeee
garik1379 [7]
The answer to how many batches is 9, hope this helped.
4 0
3 years ago
Total surface area of a cube is 1014cm^2. It's volume will be :
Karolina [17]

Answer:

Option A (2197 cm³)

Step-by-step explanation:

For a cube with length of each side "a" , it's

  • Total Surface Area = 6a²
  • Volume = a³

_____________________________________________

According to the question ,

Total Surface Area = 1014 cm²

Let the length of each side of cube be 'a'.

Using the formula ,

6a^{2} =1014

=> a^{2} =\frac{1014}{6} = 169

=> a = \sqrt{169} = +13 \: or  -13

But length can't be negative . So , length of each side = 13 cm

∴ Volume of cube = 13³ = 2197 cm³

8 0
3 years ago
At a certain store, 55 television sets were sold in April. They want to increase sells by 30% in May. How many TVs must the sale
kari74 [83]

Answer:

Step-by-step explanation:

55(1.00 + 0.30) = 71.5 so 72 sets

5 0
2 years ago
How many cars are sold in a typical week at the dealership?
nirvana33 [79]
Maybe around 10 this is a tricky question.


Different dealerships sell different amounts
6 0
3 years ago
Other questions:
  • Find the slope of this table.
    8·1 answer
  • Write an expression that is equivalent to 4(b+2)-3b
    5·2 answers
  • The product of 7/16, 4/3, and 1/2 is A. 2 13/48. B. 21/32. C. 7/24. D. 7/12.
    10·2 answers
  • What is the volume of a cube with side lengths that measure 8 cm?
    15·2 answers
  • N^2-4n-32..............
    7·1 answer
  • If the perimeter of a square is 52cm what is the area
    9·1 answer
  • Can someone help me with this
    7·2 answers
  • What is the percent of increase from 6 to 9? Write your answer using a percent sign (%)
    6·2 answers
  • How many solutions does this system have? 5y = x - 9 4x - 10y = 18<br><br> plzzz i need answer now
    9·1 answer
  • Please help! I need the answer now!!!!!!!!!
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!