Question

(Help with this Please?)

Answer 1

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:

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