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IgorLugansk [536]
2 years ago
12

The dimensions of a rectangular prism are shown below: Length: 2 1/4 ft, Width: 1 ft Height: 1 1/4 ft The lengths of the sides o

f a small cube are 1/4 foot each. Part A: How many small cubes can be packed in the rectangular prism? Show your work. (5 points) Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube. (5 points)
Mathematics
1 answer:
xenn [34]2 years ago
7 0

Answer: A. 36 small cubes

B. 36 (small ft)^3

9/16 ft^3

Step-by-step explanation:

A. 2 1/4 * 1 * 1/4 =

(8+1)/4 * 1/4=

9/4*1/4=9/16.

Small cube: 1/4*1/4*1/4=1/64

9/16=

9*4/(16*4)=36/64

36/64 / 1/64=

36/64 * 64=36 small cubes

B. 36 small cubes ==> 36 (small ft)^3

2 1/4 * 1 * 1/4 =

(8+1)/4 * 1/4=

9/4*1/4=9/16 ft^3

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I don't know why its correct. Help explain to me pls.
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The rectangle they give you is 12 units tall. This is the result of scaling by a factor of 1.5, ie it is 1.5 times taller than what the answer will be. Let the answer rectangle have a height of h. This means h*1.5 = 12, or 1.5h = 12

Divide both sides by 1.5 to find that h = 8. The answer rectangle's height is 8 units.

The width's will be treated in a similar manner. I picked on the height since it's easier to see that the height lines up with 12 (the width seems to be between 2 and 4, but its not clear if its at the midpoint).

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Answer:

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It sounds like you are asked to estimate it. That's a very valuable skill.

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