Question

BLEM SOLVING ARCHAEOLOGY At the ruins of Caesarea, archaeologists discovered a huge hy draulic concrete block with a volume of 945 cubic meters. The block's dimensions are x meters high by 12x-15 meters long by 12x-21 meters wide. What is the height of the block?

Answer 1

The height of the concrete block can be found by setting up and solving the cubic equation derived from the provided volume and dimensions of the block.

Step-by-step explanation:

The question asks to determine the height of a hydraulic concrete block with given dimensions and volume. The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, we have the volume (V) as 945 cubic meters and the dimensions given by x meters in height, (12x - 15) meters in length and (12x - 21) meters in width.

To find the height of the block, we set up the equation:

V = height x length x width

945 = x(12x - 15)(12x - 21)

We then solve this cubic equation for x to find the height of the block.