Answer:
Sophie's pyramid is approximately 4.8 inches.
Explanation:
The formula for the volume of a square pyramid is given by:
V = (1/3) * B * h
where V is the volume, B is the area of the base, and h is the height of the pyramid.
We are given that the volume of Sophie's pyramid is 90 cubic inches, and the base has a side length of 7.5 inches. The area of the base is:
B = (7.5)^2 = 56.25 square inches
Substituting these values into the formula for the volume, we get:
90 = (1/3) * 56.25 * h
Multiplying both sides by 3, we get:
270 = 56.25 * h
Dividing both sides by 56.25, we get:
h = 4.8 inches (rounded to one decimal place)
Therefore, the height of Sophie's pyramid is approximately 4.8 inches.