The dimensions of a rectangular prism are shown below: Length: 1 1/2 feet
Width: 1 foot
Height: 2 1/2 feet

The lengths of the sides of a small cube are 1/2 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

Number of small cubes that can be packed in the prism is 30 small cubes

The volume of the rectangular prism in terms of the small cube and a unit cube is 15/4 ft^3

The formula for calculating the volume of a rectangular prism is expressed as:

V = lwh

l is the length

w is the width

h is the height

Given the following

Length: 1 1/2 feet

Width: 1 foot

Height: 2 1/2 feet

V = 3/2 * 1 * 5/2

Volume  = 15/4 ft^3

Similarly, for the cube;

Volume of the small cube = l³ = (1/2)³ = 1/8 ft^3

a) Number of small cubes that can be packed in the prism  = 15/4 * 8

Number of small cubes that can be packed in the prism = 30 small cubes

b) The volume of the rectangular prism in terms of the small cube and a unit cube = 1/8 * 30 cubes

The volume of the rectangular prism in terms of the small cube and a unit cube is 15/4 ft^3

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Step-by-step explanation:

The volume of the rectangular prism = l × b × h

= 1 1/2 × 1 × 2 1/2

= 3/2 × 5/2

= 15/4 feet³

The volume of the small cube = (1/2)³

= 1³/2³

= 1/8 foot³

To find:

How many small cubes fit in the rectangular prism?

15/4 ÷ 1/8

15/4 × 8

15 × 2

30

Therefore, 30 small cubes can fit inside the rectangular prism.

The volume of the rectangular prism in terms of the small cube

= 1/8 × 30

= 1/4 × 15

= 15/4 feet³

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square