Find the volume of a pyramid with a square base, where the side length of the base is 11.1 m and the height of the pyramid is 8.2 m. Round your answer to the nearest
tenth of a cubic meter.

336.8 cubic meter or 336.8m³

Step-by-step explanation:

In other to solve the above question we would be using the volume of a square based pyramid.

The formula for the volume of a square based pyramid is

1/3a²h

In the above question we are given the following values as:

Side length of the base = a = 11.1 m

Height of the pyramid = h = 8.2m

Volume of the square based pyramid = 1/3 × 11.1² × 8.2

= 336.774 cubic meter or 336.774 m³

Approximately to the nearest tenth = 336.8 cubic meter or 336.8m³

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt