the complete answers in the attached figure
Part 1) we have

Find the height h

Find the volume
![V=\frac{1}{3}\pi[R^{2} +r^{2} +Rr]h\\\\ V=\frac{1}{3}\pi[8^{2} +4^{2} +8*4]\sqrt{20}\\ \\ V=\frac{1}{3}\pi[112]\sqrt{20}\\ \\ V=524.52 cm^{3}](https://tex.z-dn.net/?f=%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5BR%5E%7B2%7D%20%2Br%5E%7B2%7D%20%2BRr%5Dh%5C%5C%5C%5C%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5B8%5E%7B2%7D%20%2B4%5E%7B2%7D%20%2B8%2A4%5D%5Csqrt%7B20%7D%5C%5C%20%5C%5C%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5B112%5D%5Csqrt%7B20%7D%5C%5C%20%5C%5C%20V%3D524.52%20cm%5E%7B3%7D%20)
Find the lateral area

the answer Part 1) is
a) the volume is equal to 
b) The Lateral area is equal to 
Part 2) we have

Find the slant height L

Find the lateral area

the answer part 2) is
a) The Lateral area is equal to 
Part 3) we have

Step 1
Find the values of R and r

![V=\frac{1}{3}\pi[R^{2} +r^{2} +Rr]h](https://tex.z-dn.net/?f=%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5BR%5E%7B2%7D%20%2Br%5E%7B2%7D%20%2BRr%5Dh%20)
substitute
in the formula above
![V=\frac{1}{3}\pi[(3r)^{2} +r^{2} +(3r)*r]*3](https://tex.z-dn.net/?f=%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5B%283r%29%5E%7B2%7D%20%2Br%5E%7B2%7D%20%2B%283r%29%2Ar%5D%2A3%20)
![V=\frac{1}{3}\pi[7r)^{2}]*3](https://tex.z-dn.net/?f=%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5B7r%29%5E%7B2%7D%5D%2A3%20)
![52\pi =\pi [7r^{2} ]\\ r^{2} =\frac{52}{7} \\ \\ r=2.73 ft](https://tex.z-dn.net/?f=%2052%5Cpi%20%3D%5Cpi%20%5B7r%5E%7B2%7D%20%5D%5C%5C%20r%5E%7B2%7D%20%3D%5Cfrac%7B52%7D%7B7%7D%20%5C%5C%20%5C%5C%20r%3D2.73%20ft%20)

Step 2
Find the slant height L

Step 3
Find the lateral area

the answer Part 3) is
a) The lateral area is equal to 
Part 4) we have

Find the slant height L

Find the lateral area

Find the volume
![V=\frac{1}{3}\pi[R^{2} +r^{2} +Rr]h\\\\ V=\frac{1}{3}\pi[33^{2} +15^{2} +33*15]24\\ \\ V=\frac{1}{3}\pi[112]24\\ \\ V=142.83 in^{3}](https://tex.z-dn.net/?f=%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5BR%5E%7B2%7D%20%2Br%5E%7B2%7D%20%2BRr%5Dh%5C%5C%5C%5C%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5B33%5E%7B2%7D%20%2B15%5E%7B2%7D%20%2B33%2A15%5D24%5C%5C%20%5C%5C%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5B112%5D24%5C%5C%20%5C%5C%20V%3D142.83%20in%5E%7B3%7D%20)
the answer is
a) The lateral area is equal to 
b) the volume is equal to 
Part 5) we have

Step 1
Find the value of (R-r)


Step 2
Find the value of slant height L

Step 3
Find the lateral area

Step 4
Find the total area
total area=lateral area+area of the top+area of the bottom
Area of the top

Area of the bottom

Total surface area

the answer is
a) The total surface area is 
Part 6)
Part a) Find the volume of the water tank
we have
Step 1
Find the volume
the answer Part a) is
Part b) Find the volume of the wetted part of the tank if the depth of the water is 5 ft
by proportion find the radius R of the upper side for h=5 ft

Find the volume for 
the answer Part b) is 
Part 7) we have

Step 1
Find the value of R and the value of r


Step 2
Find the value of lateral area

Step 3
Find the slant height

Find the altitude of the frustum

the answer Part a) is
the slant height is 
the answer Part b) is
the altitude of the frustum is 