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lions [1.4K]
4 years ago
7

A shipping company is loading cube shaped crates into a larger cube shaped container the smaller cubes have side lengths 21/2 fe

et,and the larger shipping container has side lengths of 10 feet. How many crates will fit in the largest shipping container?Explain your reasoning
Mathematics
1 answer:
zheka24 [161]4 years ago
7 0

Answer:

64 crates

Step-by-step explanation:

Smaller Cube Side Length = 2 1/2 feet, or, 2.5 feet

Larger Container (Cube) Side Length = 10 feet

We find volume of larger container and find volume of small crates. We divide the large volume by volume of each crate. This will give us number of crates we can fit.

Volume of Cube = x^3

Where x is the side length of the cube

Now,

Small Crate Volume = (2.5)^3 = 15.625 cubic feet

Large Container Volume = 10^3 = 1000 cubic feet

Number of crates that would fit = 1000/15.625 = 64

So, 64 crates will fit in the largest shipping container

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Question 1:

We have a 45-45-90 right triangle with the hypotenuse being the length from one corner to the opposite corner.

Multiply 30 ft with the square root of 2 and use a calculator to help give you numerical value to get your answer.

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Your answer is the second choice.

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The equilateral triangle can be divided into 2 30-60-90 triangles with the longer leg being the altitude. To get half of the side length of the right triangle, divide the altitude by the square root of 3.

\dfrac{15}{ \sqrt{3} }=\dfrac{15 \sqrt{3} }{3}=5 \sqrt{3}

The full side length is double of that, which is 10 \sqrt {3}.

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