Question

Some ice sculptures are made by filling a mold with water and then freezing it. A pyramid shaped mold has a height that is 1 foot greater than the length of each side of its square base. The volume of the ice sculpture is 4 cubic feet. What are the dimensions of the mold

Answer 1

Answer:

The dimensions of the base of the mood is square, given by 2 ft by 2 ft

And the height of the mood = 3 ft.

Explanation:

Volume of a pyramid = (1/3)(Area of base)(perpendicular height)

Let the length of the square base be b

Let the perpendicular height be h

Area of base = b²

Perpendicular height = h = b+1

Volume of the pyramid = 4 ft³

4 = (1/3)(b²)(b+1)

12 = b²(b+1)

b³ + b² = 12

b³ + b² - 12 = 0

Solving the polynomial,

b = 2 ft or -1.5 ft

And since dimensions cannot be negative,

b = 2 ft.

The height of the mood = b + 1 = 3 ft