The Washington Monument Word Problem Help

Question

The Washington Monument is 555 feet tall. The monument is composed of a 500-foot-pillar topped by a 55-foot pyramid. The base of the pillar is 55 feet wide. The base of the pyramid is 34 feet wide. Approximate the sope of the sides of the pillar and the slope of the pyramid.

Answer 1

The formula for slope is (y2-y1) / (x2-x1), where y1=initial height, y2=final height, x1=initial base, x2=final base.

PILLAR:

The initial height is ground level = 0 feet. Final height for the pillar is 500 feet. Thus y2-y1 = 500-0 = 500 feet.

The initial base is 55 feet and the final base is 34 feet. The difference is -21 feet, but because of the pillar's symmetry, we need to use 1/2 the differences in bases which is -10.5 feet. Why minus? The reason is that the pillar tapers from bottom to top.

The slope of any one of the 4 sides of the pillar is 500 / -10.5 = -47.62. This means that for every 1 foot decrease in base, the height increases by 47.62 feet.

PYRAMID:

The initial height is 500 feet and the final height is 555 feet. The difference in height is 555-500 = 55 feet.

The initial base is 34 feet and the final base is 0 feet. The difference in base is 0-34 = -34 feet, but use only 1/2 of this value = -17 feet.

The slope of any of the 4 sides of the pyramid is 55 / -17 = -3.24. This means that for every decrease in base of 1 foot, the height increases by 3.24 feet.