# A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x, y, and z to be the length, width, and height, respectively, of the box in meters. Then we wish to maximize V

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

## Related Questions

The statement B is true the corresponding lines are proportional and the angles are congruent. The question with graph is A. AB with MN; BC with NL; AC with NL

Show us the maze and we will help

Three teams, A, B and C, play in a competition.games won by A: games won by B = 3:1
games won by B: games won by C = 4:3
Team B has won 8 games.
In total, how many games have the three teams won?

A = 24

B = 8

C = 6

Step-by-step explanation:

4:3 from B:C

8:6

8 games won by B and 6 games won by C.

3:1 from A:B

24:8

24 by A and 8 by B

Team A won 24 games, Team B won 8 games and Team C won 6 games. So, the total games won by all three teams is 38.

### Explanation:

From the problem, we know that the ratio of games won by Team A to Team B is 3:1, and the ratio of games won by Team B to Team C is 4:3. We also know that Team B has won 8 games.

Since the ratio of Team B to Team A is 1:3, Team A must have won 3 times as many games as Team B. Therefore, Team A has won 3 * 8 = 24 games.

The ratio of games won by Team B to Team C is 4:3. This means Team B won 4 games for every 3 games Team C won. Since Team B won 8 games, Team C must have won 3/4 as many games as Team B. Therefore, Team C won 3/4 * 8 = 6 games.

So, in total, the three teams won 24 + 8 + 6 = 38 games.

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Mr. Gordon has 13 girls and 14 boys in his fourth period algebra class. One person is chosen at random.What is the probability that the person chosen is a boy?
A. 1/14
B. 1/27
C. 13/14
D. 13/27
E. 14/27

The probability that the person chosen is a boy is 14/27.

Number of girls = 13

Number of boys = 14

Total students = 27

### What is probability?

Probability is a measure of the likelihood of occurrence of an event.

P(event) = Favorable outcomes / total outcomes

Favourable outcomes = 14 because there are 14 boys

Total outcomes =27

So, the probability that the person chosen is a boy will be given by:

P(boy)=14/27

So, the probability that the person chosen is a boy is 14/27.

Hence, the probability that the person chosen is a boy is 14/27.

To get more about probability visit:

brainly.com/question/24756209

E

Step-by-step explanation:

It's E because you have to add 13 and 14 and as you can see there's 14 boys so it's E.

HELP MEE ILL MARK BRAINLEIST

3x-3 I think that's it.

Step-by-step explanation:

The vertex is (1, -4)

Step-by-step explanation:

Simplify the expression 7(1 +5v) =​

the answer is 7 + 35v