Mathematics, 01.04.2020 20:03, playboib

A sheet of copper is twice as long as it is wide. From each corner a 3 inch square is cut out, and the end ends are then turned up to form a tray. If the volume of the tray is 324 cubic inches, what were the original dimensions of the sheet if copper.

Answers: 2

Show answers

Answers

answered: kingk7368

The original length of the sheet = 24 inches

The original width of the sheet = 12 inches

Step-by-step explanation:

Let us denote the original width of the sheet of the copper by "x". Since the length of that sheet of copper is twice as long as it is wide (width), then the length of this sheet of copper (rectangle) should be "2x".

Now, since 3 inch squares were cut out at the four ends of the rectangular sheet of copper, then the new length of the copper should be 2x - 6 inches.

Reason:- A rectangle has 4 sides. Two of the sides are the length and the remaining two sides are the width or breadth. Now, for one of the sides (length), two 3 - inch squares from the two ends are cut out. This means that each of the length sides will lose (3 inches + 3 inches = 6 inches).

The new width of the rectangular sheet of copper will then be x - 6 inches (the same reason as the length).

Later the ends are then turned up to form a tray. This means that the height of the tray will now become 3 inches.

Since the volume of this tray (cuboid shape) is 324 cubic inches, we can calculate the original dimensions of the sheet:-

Volume of a cuboid = L*w*h

L = 2x - 6

w = x - 6

h = 3

Then:

(2x - 6)(x - 6) × 3 = 324

(2x^2 - 12x - 6x + 36) × 3 = 324

(2x^2 - 18x + 36) × 3 = 324

6x^2 - 54x +108 = 324

6x^2 - 54x + 108 - 324 = 0

6x^2 - 54x - 216

Divide through by 6

= x^2 - 9x - 36

We will now solve for x using any formula or method of solving quadratic equations:

$\frac{--9+-\sqrt{(9^{2})-(4*1*-36) } }{2*1}$

$\frac{9+-\sqrt{225} }{2}$

$\frac{9+15}{2} = 12$

$\frac{9-15}{2} = -3$

x = - 3 or 12

Since x = a positive integer then the width of the rectangular sheet of copper was 12 inches originally.

The length = 2x

Therefore the length = 2 × 12 = 24 inches.

L = 24 inches

w = 12 inches.

answered: Guest

3100

step-by-step explanation:

answered: Guest

answer: i dont know but if you try hard you will get it right : )

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:00, moonk7733

What is the standard form of -5x^2+2x^4-11+x^3+3x

Answers: 2

continue

Mathematics, 21.06.2019 16:10, cuppykittyy

The probability that a college student belongs to a health club is 0.3. the probability that a college student lives off-campus is 0.4. the probability that a college student belongs to a health club and lives off-campus is 0.12. find the probability that a college student belongs to a health club or lives off-campus. tip: p(a or b) = p(a) + p(b) - p(a and b) 0.54 0.58 0.70 0.82

Answers: 2

continue

Mathematics, 21.06.2019 19:30, jasminetaylor4587

According to the data set, where should the upper quartile line of the box plot be placed?

Answers: 1

continue

Mathematics, 21.06.2019 20:30, danizara8

The sum of these consecutive integers is equal to 9 less than 4 times the least of the integer. find the three integers

Answers: 1

continue

Do you know the correct answer?

A sheet of copper is twice as long as it is wide. From each corner a 3 inch square is cut out, and t...