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
lys-0071 [83]
2 years ago
15

A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the

Mathematics
1 answer:
Vinvika [58]2 years ago
8 0

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

You might be interested in
Please help with this problem
Mkey [24]

Answer:

7×10=70

area = length × width

8 0
2 years ago
Read 2 more answers
Find the angle measure that of each missing angle
11111nata11111 [884]

Step-by-step explanation:

122+v=180

v=180-122

v=58

w+61=180

w=180-61

w=119

61+58+y=180

119+y=180

y=180-119

y=61

61+x=180

x=180-61

x=119

j=180

4 0
3 years ago
1/8 times 5/8 in simplest form
3241004551 [841]

Answer:

5/64

Step-by-step explanation:

numerators 1 time 5 is 5 and denominators 8 times 8 is 64;  5/64

8 0
2 years ago
Read 2 more answers
you have $155 in a savings account. you decide tobl add $20 to the account every week. write an expression that shows your savin
KIM [24]

Answer:155+20n

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Please help with this question!
lukranit [14]

Answer:

a. x = 5, AB = 14, BC = 8

Step-by-step explanation:

✔️Both triangles are similar, therefore their side lengths are proportional to each other.

Thus:

\frac{2x + 4}{x + 3} = \frac{7}{4}

Cross multiply

4(2x + 4) = 7(x + 3)

8x + 16= 7x + 21

Collect like terms

8x - 7x = -16 + 21

x = 5

✔️AB = 2x + 4

Plug in the value of x

AB = 2(5) + 4

AB = 14

✔️BC = x + 3

Plug in the value of x

BC = 5 + 3

BC = 8

7 0
3 years ago
Other questions:
  • In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 67 inches and a s
    7·1 answer
  • How do I solve it by substitution?<br>y=-2<br>4x-6y=-20
    11·2 answers
  • Sally has a candy bar. if she gives 2/5th of the bar to mark and mark gives 1/2 of his piece to john, what percentage of the ori
    7·1 answer
  • Solve for x<br> -4 = x - 7
    11·2 answers
  • A taxi company charges passengers $2.00 for a ride, and an additional $0.50 for each mile traveled. The function rule = 0.50 + 2
    15·1 answer
  • Given: AB with point C between A and B. AB = 10x + 20, AC = 2x + 13, and CB = 10x - 9.
    7·1 answer
  • Describe the value of the 9 in 926,415 use at least 2 terms from the word list in your explanation
    13·1 answer
  • Decimal multiplier by 1.7%
    6·2 answers
  • PLZ HELP ME WITH THIS ONE ALSO :)
    10·1 answer
  • You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of ​claves, and x djembe
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!