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777dan777 [17]
3 years ago
12

(Help with this Please?)

Mathematics
1 answer:
Yakvenalex [24]3 years ago
4 0

Answer:

A) 30 cubes.

B) 30 units³.


Step-by-step explanation:

A) 1. Calculate the volume of the rectangular prism, as following:

Vr=(lenght)(width)(height)

2. You have that:

- The length is: 1^{\frac{1}{2}}ft=1.5ft

- The width is: 1ft

- The heigth is: 2^{\frac{1}{2}}ft=2.5ft

3. Substitute these values into the formula:

Vr=(1.5ft)(1ft)(2.5ft)=3.75ft^{3}

4. The volume of one cube is:

Vc=side^{3}

5. The length of one side is: \frac{1}{2}ft=0.5ft

6. Substitute this value into the formula:

Vc=(0.5ft)^{3}=0.125ft^{3}

7. The number of small cubes that can be packed in the rectangular prism is:

cubes=\frac{Vr}{Vc}\\cubes=\frac{3.75ft^{3}}{0.125ft^{3}}\\cubes=30

B) 1. The length, the width and the height of the rectangular prism in term of units cubes is:

Length=\frac{1.5ft}{0.5ft}=3units

Width=\frac{1ft}{0.5ft}=2units

Heigth=\frac{2.5ft}{0.5ft}=5units

2. Therefore, the volume of the rectagular prism in terms of the small cube and a unit cube is:

Vr=(3units)(2units)(5units)=30units^{3}

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