A prism has a length of 8 meters, height of 14 meters, and width of 6 meters. What is the volume of the prism? m3

672 m^3

Step-by-step explanation:

The formula to find the volume of a prism is V = l x w x h, where l is length, w is width, and h is height. You are given the length, width, and height in the problem so you just plug it into the formula.

V = 8 x 6 x 14

After multiplying all three numbers together, you should get the answer 672 m^3.

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