The volume of the pyramid is 2496 cu.m.
<h3>What is a Pyramid ?</h3>
A pyramid is a three dimensional structure which has a polygon base and in general triangular faces which join at the top .
It is given that
A pyramid 
has a 4 m by 4 m square top
Height = 12 m
Base = 20 m
The volume of a square pyramid with a is given by
V = (1/2) * ( Area of base + Area of ) * height of the from the base
V = 0.5 * ( 20 *20 + 4*4 ) * 12
V = 2496 cu.m
The volume of the pyramid is 2496 cu.m.
To know more about Pyramid
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Solution :
From the table,
Number of countries = 
Mean = 
Standard deviation = 
Margin of error of B = 50,000 acres
So we determine the 
and then allocate the four regions of 
and 
.
Under the 
, the 
for the value of 
which yields 
is given by :
Let us complete the numerator
= 453329920
The bound on the error of estimation is B = 50,000 acres
Hence we get
= 625,000,000
= 220.24044
≈ 221 (approximately)
Therefore, the sample size under the proportional allocation from each stratum are given by :
![$n_1=n\left[\frac{N_1}{\sum_{K=1}^\mu N_K}\right]$](https://tex.z-dn.net/?f=%24n_1%3Dn%5Cleft%5B%5Cfrac%7BN_1%7D%7B%5Csum_%7BK%3D1%7D%5E%5Cmu%20N_K%7D%5Cright%5D%24)
![$=221\left[\frac{1052}{3056}\right]$](https://tex.z-dn.net/?f=%24%3D221%5Cleft%5B%5Cfrac%7B1052%7D%7B3056%7D%5Cright%5D%24)
≈ 76
![$n_2=n\left[\frac{N_2}{\sum_{K=1}^\mu N_K}\right]$](https://tex.z-dn.net/?f=%24n_2%3Dn%5Cleft%5B%5Cfrac%7BN_2%7D%7B%5Csum_%7BK%3D1%7D%5E%5Cmu%20N_K%7D%5Cright%5D%24)
![$=221\left[\frac{210}{3056}\right]$](https://tex.z-dn.net/?f=%24%3D221%5Cleft%5B%5Cfrac%7B210%7D%7B3056%7D%5Cright%5D%24)
≈ 15
![$n_3=n\left[\frac{N_3}{\sum_{K=1}^\mu N_K}\right]$](https://tex.z-dn.net/?f=%24n_3%3Dn%5Cleft%5B%5Cfrac%7BN_3%7D%7B%5Csum_%7BK%3D1%7D%5E%5Cmu%20N_K%7D%5Cright%5D%24)
![$=221\left[\frac{1376}{3056}\right]$](https://tex.z-dn.net/?f=%24%3D221%5Cleft%5B%5Cfrac%7B1376%7D%7B3056%7D%5Cright%5D%24)
≈ 100
![$n_4=n\left[\frac{N_4}{\sum_{K=1}^\mu N_K}\right]$](https://tex.z-dn.net/?f=%24n_4%3Dn%5Cleft%5B%5Cfrac%7BN_4%7D%7B%5Csum_%7BK%3D1%7D%5E%5Cmu%20N_K%7D%5Cright%5D%24)
![$=221\left[\frac{418}{3056}\right]$](https://tex.z-dn.net/?f=%24%3D221%5Cleft%5B%5Cfrac%7B418%7D%7B3056%7D%5Cright%5D%24)
≈ 30
Thus, we should select 76 counties from North central region, 15 counties from the north east region, 100 from south region and 30 from west region.
We can also estimate mean acreage of each county across all the county with a margin of error of 50,000 acres.
Answer:
53
Step-by-step explanation:
