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AlexFokin [52]
3 years ago
15

Cube-shaped blocks are packed into a cube-shaped storage container. The edge of the storage container is 2 1/2 feet. The edge le

ngth of each block is 1/5 the edge length of the storage container. What is the volume, in cubic feet, of one cube-shaped block?
Mathematics
1 answer:
GarryVolchara [31]3 years ago
4 0

Answer:

Volume of one cube shaped block is, 0.125 cubic feet

Step-by-step explanation:

Volume of a cube(V) is given by:

V = a^3                 .....[1]

where a is the edge length of the cube.

As per the statement:

Cube-shaped blocks are packed into a cube-shaped storage container. The edge of the storage container is 2 1/2 feet.

⇒\text{Edge length of storage} = 2\frac{1}{2} = 2.5 ft

It is also given that:

The edge length of each block is 1/5 the edge length of the storage container

⇒\text{Edge length of each block (a)} = \frac{1}{5} \cdot 2.5 = 0.5 ft

Substitute this in [1] we have;

V = (0.5)^3 = 0.125 ft^3

Therefore,  volume, in cubic feet, of one cube-shaped block is, 0.125

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The coordinates of the vertices of a rectangle are (−3, 4) , (7, 2) , (6, −3) , and (−4, −1) . What is the perimeter of the rect
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Answrer

Find out the what is the perimeter of the rectangle .

To prove

Now as shown in the figure.

Name the coordinates as.

A(−3, 4) ,B (7, 2) , C(6, −3) , and D(−4, −1) .

In rectangle opposite sides are equal.

Thus

AB = DC

AD = BC

Formula

Disatnce\ formula = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2}}

Now the points  A(−3, 4) and  B(7, 2)

AB = \sqrt{(7- (-3))^{2} +(2- 4)^{2}}

AB = \sqrt{(10)^{2} +(-2)^{2}}

AB = \sqrt{100+4}

AB = \sqrt{104}

AB = 2\sqrt{26}\units

Thus

CD= 2\sqrt{26}\units

Now the points

A (−3, 4) , D (−4, −1)

AD = \sqrt{(-4 - (-3))^{2} +(-1- 4)^{2}}

AD = \sqrt{(-1)^{2} +(-5)^{2}}

AD = \sqrt{1 + 25}

AD = \sqrt{26}\units

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Formula

Perimeter of rectangle = 2 (Length + Breadth)

Here

Length = 2\sqrt{26}\ units

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Perimeter\ of\ rectangle = 2(2\sqrt{26} +\sqrt{26})

Perimeter\ of\ rectangle = 2(3\sqrt{26})

Perimeter\ of\ rectangle = 6\sqrt{26}

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Perimeter\ of\ rectangle = 6\times 5.1

Perimeter of a rectangle = 30.6 units.

Therefore the perimeter of a rectangle is 30.6 units.

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Crystal has 121 compact discs. The total number of boxes required are 5.

<u>Solution:</u>

Given, Crystal has 121 compact discs that she wants to put into boxes.  

Each of the boxes that she brought home holds 25 discs.  

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Now, we know that, number of boxes required =\frac{\text {total number of discs}}{\text {capacity of one box}}=\frac{121}{25}=4.84=5

Here we took 5 because 0.84 means that box with discs less than 25 still we require a box.  

Hence, the total number of boxes required are 5.

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3 years ago
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