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The volume and surface area of this square pyramid is approximately 277.33 and 281.6 respectfully.

Step-by-step explanation:

To find the volume of a pyramid, you need to multiply the base area by the vertical height and divide it by 3. In this case, the volume of the square pyramid would be = = ≈ 277.33 . If you want to find the surface area of a shape, you have to calculate the area of every side making up the 3-dimensional figure and add them all together to figure out the surface area. In this case, the surface area would be = = = = 281.6 . So the volume of the square pyramid would be approximately 277.33 , and the surface area is 281.6 .

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