All categories

1 year ago

it takes 126 cubes that have edge lengths of 1/3feet to completely fill this plastic bin what is the area of the base of bin

Mathematics

2 answers:

8_murik_8 [283]1 year ago

6 0

Answer: 1) Each of the 126 cubes has a volume = (1/3)3 = 1/3 × 1/3 × 1/3 = 1/27 cubic feet.

2) It takes 126 cubes to fill the bin, so the bin has a volume of 126 × 1/27 = 126/27 cubic feet. (Don't do this division yet - leave it as an improper fraction)

3) The volume of the bin is also given by the formula Volume = Area of Base × Height. Plus we know the volume is 126/27 cubic feet and the height is 2 1/3 = 7/3 of a foot, so:

Step-by-step explanation: Volume = Area of Base × Height

126/27 = Area of Base × 7/3

126/27 × 3/7 = Area of Base

Arada [10]1 year ago

4 0

The area of the base of bin is 2 feet².

<h3>What is Volume of Cube?</h3>

The formula of volume of the cube is given by: Volume = a³, where a is the length of its sides or edges.

Given:

Edge = 1/3 feet

Volume of 1 cube= l³= (1/3)³ = 1/27

Totals cubes= 126

So, Volume of 126 cube= 126 x 1/27 = 126/ 27

Then, Volume of Plastic Bin= Area of base x height

126 / 27 = Area of base x 7/3

Area of base = 126 /27 x 3 /7

Area of base = 2 ft²

Learn more about volume of cube here:

brainly.com/question/11168779

#SPJ2

You might be interested in

Range of f(x)=-(x-5)^2+9

svet-max [94.6K]

Answer: (5, -9)

Step-by-step explanation:

Rewrite the equation in term of x and y.

7 0

3 years ago

If 3x+2y=18 find x and y for which the product xy takes its maximum value

grin007 [14]

Answer:

(x, y) = (3, 4.5)

Step-by-step explanation:

You want to find x and y such that xy is a maximum subject to the constraint that 3x+2y=18.

<h3>Objective function</h3>

The objective function f(x, y) = xy is most easily maximized if it can be written in terms of one variable only. Solving the constraint equation for y, we have ...

3x +2y = 18

2y = 18 -3x

y = 1/2(18 -3x) = (3/2)(6 -x)

Then the objective function is ...

f(x) = x(3/2)(6 -x)

<h3>Maximum</h3>

We recognize this as the equation of a parabola that opens downward, and has zeros at x=0 and x=6. Its line of symmetry is halfway between those, at x = 3. That is the location of the maximum of the objective function.

The corresponding y-value is ...

y = (3/2)(6 -3) = 9/2 = 4.5

The values of x and y that maximize their product are (x, y) = (3, 4.5).

<em>Additional comment</em>

In the attached graph, the larger the product, the farther away the curve is from the origin. The product is maximized subject to the constraint when the curves are tangent to each other. That point of tangency is (x, y) = (3, 4.5).