What is the Surface area and volume of all the parts of the castle?
Accepted Solution
A:
N 1 FRONT LEFT TOWER
[surface area of a prism]=[area of the base]+perimeter*h------> only one base [surface area of a prism]=[3*3]+[4*3]*50----> 609 units²
[surface area of a triangular pyramid]=[area of the 4 triangles]----> without base [area of 1 triangle]=3*h/2 h²=3²+1.5²----> h²=11.25-----> h=√11.25 units [area of 1 triangle]=3*√11.25/2-----> 5.03 units² [surface area of a triangular pyramid]=[4*5.03]-----> 20.12 units²
surface area of the front left tower=609+20.12-----> 629.12 units²
[volume of a prism]=[3*3*50]=450 units³ volume of a triangular pyramid]=[area of the base]*h/3 volume of a triangular pyramid]=[3*3]*3/3-----> 9 units³
[volume of the front left tower]=450+9------> 459 units³
N 2 FRONT RIGHT TOWER
[surface area of a cylinder]=[area of the base]+perimeter*h--> only one base [surface area of a cylinder]=[pi*3²]+[2*pi*50]--> 342.26 units²
[surface area of a cone]=pi*r*l------> without base r=3 units l²=r²+h²-----> 3²+3²-----> 18---------> l=√18 units [surface area of a cone]=pi*3*√18------> 39.97 units²
surface area of the front right tower=342.26+39.97------> 382.23 units²
[volume of a cylinder]=pi*r²*h [volume of a cylinder]=pi*3²*50-----> 1413 units³
[volume of a cone]=pi*r²*h/3 [volume of a cone]=pi*3²*3/3----> 28.26 units ³
[volume of the front right tower]=1413+28.26-----> 1441.26 units³
N 3 BACK LEFT TOWER [surface area of a cylinder]=[area of the base]+perimeter*h--> only one base [surface area of a cylinder]=[pi*3²]+[2*pi*50]--> 342.26 units²
[surface area of hemisphere]=2*pi*r² [surface area of hemisphere]=2*pi*3²-------> 56.52 units²
surface area of the back left tower=342.26+56.52-----> 113.04 units²
[volume of a cylinder]=pi*r²*h [volume of a cylinder]=pi*3²*50-----> 1413 units³
[volume of a hemisphere]=(4/6)*pi*r³ [volume of a hemisphere]=(4/6)*pi*3³-----> 56.52 units³
[volume of the back left tower]=1413+56.52-------> 1469.52 units³
N 4 BACK RIGHT TOWER [surface area of a triangular prism]=[area of the base]+perimeter*h------> only one base
find the area of the base h²=3²-1.5²-----> h=√6.75 [area of the base]=3*√6.75/2----> 3.90 units² [surface area of a triangular prism]=[3.90]+[3*3*50]-----> 453.9 units²
[surface area of a triangular pyramid]=[area of the 3 triangles]----> without base [area of 1 triangle]=3*h/2 h²=3²+1.5²----> h²=11.25-----> h=√11.25 units [area of 1 triangle]=3*√11.25/2-----> 5.03 units² [surface area of a triangular pyramid]=[3*5.03]-----> 15.09 units²
surface area of the back right tower=453.9+15.09-----> 468.99 units²
[volume of a triangular prism]=area of the base *height find the area of the base h²=3²-1.5²-----> h=√6.75 [area of the base]=3*√6.75/2----> 3.90 units² [volume of a triangular prism]= 3.90*50------> 195 units³
volume of a triangular pyramid]=[area of the base]*h/3 volume of a triangular pyramid]=[3.90]*3/3------> 3.90 units³
[volume of the back right tower]=195+3.90------> 198.90 units³
N 5 CENTRAL BUILDING
[surface area]=2*[area of the base]+perimeter of the base *heigth [surface area]=100*50*2+2*(150)*30-----> 10000+9000-----> 19000 units²
surface area of the central building=19000 units²
volume of the central building =100*50*30-----> 150000 units³
volume of the central building=150000 units³
N 6 total surface area=629.12+382.23+113.04+468.99+19000-----> 20593.38 unit² total volume=459+1441.26+1469.52+198.90+150000------> 153568.68 units³