Volume of cube = ( side)^3
Side = 6 feet = 6×12 = 72 inches ( 1ft =12 inch)
Vol. = (72)^3 = 72×72×72= 373248 cubic inches
1 gallon = 4 quarts
1 quart = 32 ounces
1 gallon = 128 ounces
9 gallons = 1,152 ounces
Filling 8 ounce cups = 1,152 / 8 = 144 cups
Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:
![\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac2n%5Cright%5D%2C%5Cleft%5B%5Cdfrac2n%2C%5Cdfrac4n%5Cright%5D%2C%5Cleft%5B%5Cdfrac4n%2C%5Cdfrac6n%5Cright%5D%2C%5Cldots%2C%5Cleft%5B%5Cdfrac%7B2%28n-1%29%7Dn%2C2%5Cright%5D)
Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,
where 
. Each interval has length 
.
At these sampling points, the function takes on values of
We approximate the integral with the Riemann sum:
Recall that
so that the sum reduces to
Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:
Just to check:
The total weight of the liquid that filled the hemispheric tank to the nearest full pounds is 66775 pounds.
<h3>What is the volume of an hemisphere?</h3>
An hemisphere is half of a sphere. Therefore,
volume = 2 / 3 πr³
where,
Therefore,
r = 7 feet
volume = 2 / 3 × 3.14 × 7³
volume = 2 / 3 × 3.14 × 343
volume = 2154.04 / 3
volume = 718.013333333
volume = 718.013
Therefore,
density = mass / volume
93 = mass / 718.013
mass = 718.013 × 93
mass = 66775.24
mass ≈ 66775 pounds
learn more on hemisphere here: brainly.com/question/14527816
