A diagram of a rectangular prism filled with unit cubes is shown below. Each unit cube has

1 answer:

7 0

The volume of the rectangular prism filled with unit cubes each measuring the value of the length given is 72ft³.

Hence, Option D) 72ft³ is the correct answer.

<h3>Rectangular Prism and Cube</h3>

A rectangular prism is simply a three-dimensional solid shape with six faces which are rectangles.

The volume of a rectangular prism is expressed as;

V = l × w × h

Where l is length, w is width and h is height of the prism

A cube is a three-dimensional solid with six equal square-shaped sides.

Given the data in the question;

Length of the sides of the cube = 1 foot

Length of the rectangular prism l = 4 cubes × 1 foot = 4ft

Width of the rectangular prism w = 3 cubes × 1 foot = 3ft

Height of the rectangular prism l = 6 cubes × 1 foot = 6ft

To determine the volume of the rectangular prism, we substitute our given values into the expression above.

V = l × w × h

V = 4ft × 3ft × 6ft

V = 72ft³

Option D) 72ft³ is the correct answer.

Hence, the volume of the rectangular prism filled with unit cubes each measuring the value of the length given is 72ft³.

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The lengths of the diagonals of a rhombus are 4x and 8x. What algebraic expression gives the perimeter of the rhombus?

Marizza181 [45]

Answer:

Approximately 17.88x or $8x\sqrt{5}$

Step-by-step explanation:

Use pythagorean formula. In a rhombus the diagonals bisect each other and they are perpendicular, so you could have a right triangle with legs of 2x and 4x, the hypoteneuse would then be $\sqrt{(2x)^{2} +(4x)^{2} }= \sqrt{4x^{2} +16x^{2}}$ which is approximately 4.47x. In a rhombus all 4 sides are the same, so multiply that by 4 and you get the perimeter. 4(4.47x) = 17.88x or if you simplify the radical instead it's $8x\sqrt{5}$