Question

A certain dam required approximately 850 million cubic feet of concrete. To make this number more understandable, consider it to be equivalent to the volume of a block 1 mile long, 1 mile wide, and x feet high. Solve for x.

Answer 1

The height x of a block 1 mile by 1 mile to match a volume of 850 million cubic feet, convert the dimensions to feet and solve for x, resulting in approximately 30.6 feet.

Step-by-step explanation:

To solve for x in the context of a block measuring 1 mile long, 1 mile wide, and x feet high that is equivalent to 850 million cubic feet, we need to convert the dimensions into consistent units first. Given that 1 mile is equal to 5280 feet, the volume of the block in cubic feet can be expressed as:

V = length × width × height = (5280 feet) × (5280 feet) × x feet

We then set this volume equal to the given volume of concrete, and solve for x.

850,000,000 cubic feet = 5280 feet × 5280 feet × x feet

Divide both sides by the product of the length and the width to isolate x.

x = 850,000,000 cubic feet / (5280 feet × 5280 feet)

Calculate x to find the height of the block in feet, which will make the volume more understandable.

x ≈ 30.6 feet