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algol [13]
2 years ago
5

You are building a curio cabinet in the form of a rectangular prism that must be 4 feet tall with a volume of 48 cubic feet. The

length and with each must be no more than tot. Which of the following dimensions are the possible width and length of the cabinet? a) 15 foot by feet b) 24 feet by 5 foot c) 25 feet by 4.8 feet d) 3 feet by 4 feet e) 4 feet by 12 feet 19
Mathematics
1 answer:
Mekhanik [1.2K]2 years ago
7 0

Answer:

d) 3 feet by 4 feet

Step-by-step explanation:

Volume of the prism = 48 feet³

Height if the prism = 4 feet

To determine the possible values of the length and width of the prism let's divide the volume by the height.

So 48/4 = 12

So we'll be looking for a product of two numbers to give us 12

And it's between 12 and 1, 4 and 3 , and 6 and 2.

We have only 4 and 3 in the option.

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Problem 1

<h3>Answer:  104 cubic inches</h3>

----------------------

Explanation:

The prisms are similar so they have the same shape, but different sizes.

The linear scale factor from small to large is:

large/small = 10/4 = 2.5

Meaning that we multiply each dimension of the smaller prism by 2.5 to get the corresponding side length of the larger prism

4*2.5 = 10

This linear scale factor is then cubed to get the volume scale factor

(2.5)^3 = 15.625

Which tells us:

larger volume = 15.625*(smaller volume)

smaller volume = (larger volume)/15.625

smaller volume = (1625)/15.625

smaller volume = 104 cubic inches

========================================================

Problem 2

<h3>Answer:  650 square inches</h3>

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Explanation:

We will go back to the linear scale factor of 2.5

This time, we square it to get (2.5)^2 = 6.25

This is the surface area scale factor.

larger surface area = 6.25*(smaller surface area)

larger surface area = 6.25*(104)

larger surface area = 650 square inches

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