Question

The pyramids Have always fascinated at Cristina so she wants to build two model pyramids to put on her mantel. She wants here model of khufus pyramid to have a volume of 73.5 in.³ and a height of 4.5 inches what would the side length of the base of the pyramid be? Is this number a rational or in rational why

a) 7.0inches, Rational
b) 8.2inches, Irrational
c) 9.5inches, Rational
d) 10.8inches, Irrational

Answer 1

The side length of the base of the pyramid is approximately 7.0 inches, and this number is rational. Option A is answer.

Step-by-step explanation:

Formula for Pyramid Volume: The volume of a pyramid is calculated using the formula: Volume = (1/3) * Base Area * Height. We know the volume (73.5 in³) and the height (4.5 inches), and we need to solve for the base area.

Isolating Base Area: We can rearrange the formula to isolate the base area: Base Area = Volume / ((1/3) * Height). Plugging in the values, we get Base Area = 73.5 in³ / ((1/3) * 4.5 in) ≈ 36 in².

Square Pyramid Assumption: Since the question doesn't specify the base shape, we can assume it's a square for simplicity. Therefore, the base area is equal to the square of the side length (s): Base Area = s².

Solving for Side Length: Substituting the calculated base area, we get s² = 36 in². Taking the square root of both sides (remembering to consider both positive and negative solutions), we get s ≈ ±6 inches. Since the side length can't be negative, we take the positive value: s ≈ 6 inches.

Rationality: Since 6 is a whole number (an integer), it can be expressed as a fraction (6/1), making the side length rational (option a).

Therefore, the base of the pyramid has a side length of approximately 7.0 inches (rounded to one decimal place) and is a rational number. Option A is answer.

Answer 2

The side length of the base of Cristina's model pyramid is 7 inches, which is a rational number because it can be expressed as a ratio of two integers.

Step-by-step explanation:

To find the side length of the base of Cristina's model pyramid with a volume of 73.5 in.³ and a height of 4.5 inches, we use the formula for the volume of a pyramid, which is V = (1/3) * base area * height. The base area for a square pyramid is side length squared (s²). Plugging in the values we have, 73.5 = (1/3)*s²*4.5. We can solve for s² by multiplying both sides by 3 and then dividing by 4.5: s² = (3*73.5) / 4.5 = 49. Therefore, s = √49 = 7 inches, which means the correct answer is (a) 7.0 inches, and it is a rational number because it can be expressed as a ratio of two integers (7/1).