Find the total volume of the castle including the towers answer

The complete question in the attached figure

we know that

Tower B ( lower left) 
a) Square Pyramid 
V = 1/3 lwh 
V = (1/3)(3)(3)(3) 
V = (1/3)(3)(9) 
V = (1/3)(27) 
V = 9 cubic units 
b) Rectangular Prism 
V = lwh 
V = (3)(50)(3) 
V = (3)(150) 
V = 450 cubic units 
tower B volume 
Va + Vb 
450 + 9 
459 cubic units 

Tower E (lower right) 
a) Cone 
V = 1/3 pi r^2 h 
V = (1/3)(3.14)(3^2)(3) 
V = (1/3)(3.14)(9)(3) 
V = (1/3)(3.14)(27) 
V = (1/3)(84.78) 
V = 28.26 cubic units 
b) Cylinder 
V = pi r^2 h 
V = (3.14)(3^2)(50) 
V = (3.14)(9)(50) 
V = (3.14)(450) 
V = 1,413 cubic units 
Tower E Volume 
Va + Vb 
28.26 + 1,413 
1,441.26 cubic units

Tower A (upper left) 
a) Hemisphere 
Since it is a hemisphere, divide the formula of sphere by 2. 
V = (4/3)pi r^3 all over by 2 
V = (4/3)(3.14)(3^3) all over by 2 
V = 113.04 / 2 
V = 56.52 cubic units 
b) Cylinder 
V = pi r^2 h 
V = (3.14)(3^2)(50) 
V = (3.14)(9)(50) 
V = (3.14)(450) 
V = 1,413 cubic units 
3rd Tower Volume 
Va + Vb 
56.52 + 1,413 
1,469.52 cubic units 

Tower D (upper right) 
a) Triangular pyramid 
V = 1/3(1/2 bh)(H) 
where b is base of the triangular base 
h is the height of the triangular base 
H is the altitude of the pyramid 
Since H is unknown, bisect the triangular base then use Pythagorean theorem to find H. 
a^2 + b^2 = c^2 
let a be the base of the right triangle 
b be the H or missing side of the right triangle 
c be the hypotenuse of the triangle 
(1.5^2) + (b^2) = 3^2 
2.25 + b^2 = 9 
b^2 = 9 - 2.25 
b^2 = 6.75 
b = 2.6 units 
H = 2.6 units 
Substitute: 
V = (1/3)[(1/2)(3)(2.6)](3) 
V = (1/3)[3.9](3) 
V = (1/3)(11.7) 
V = 3.9 cubic units 
b) Triangular Prism 
V = (bh/2) H 
V = [(1.5)(2.6)/2](50) 
V = (3.9/2)(50) 
V = (1.95)(50) 
V = 97.5 cubic units 
4th Tower Volume 
Va + Vb 
3.9 + 97.5 
101.4 cubic units

Main Castle 
V = lwh 
V = (100)(50)(30) 
V = (100)(1500) 
V = 150,000 cubic units 

Total Volume 
V1 + V2 + V3 + V4 + V5 
459 + 1,441.26 + 1,469.52 + 101.4 + 150,000 ------> 153,471.18 cubic units 

Therefore,

the answer is
 the volume of the castle and the towers is 153,471.18 cubic units 

65

Step-by-step explanation: