Answer:
d) 135º
Step-by-step explanation:
Note that the angle DCU is the sum of the angles DCB and BCU. The angle DCB is 90º because A B C D is a square, then all its angles are equal to 90º.
After attaching B U C to A B C D, we obtain a trapezoid A U C D. Since A U C D has at least one pair of parallel sides, then AU should be parallel to CD, thus the angle CBU must be 90º.
B U C is isoceles, so we conclude that other two angles must have the same size, and due to the sum of the angles of a triangle being 180º, then both BUC and BCU are equal to 45º
As a result, the angle DCU is equal to 90º+45º = 135º. Option d is the correct one.
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
Answer:
whats wrong
Step-by-step explanation:
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The number of feet in the length of the handrail is 17.3 ft.
The easiest way to see this is to imagine that we can "unfold" the spiral to create a rectangle
The bottom side of the rectangle is just the arc length of a circle with a radius of 3 ft turned through 270°= (3/4) of a whole revolution
(3/4) (2pi) (3) = (9/2)pi ft = 4.5 pi ft
The side of the rectangle will be the rise of the staircase = 10ft
And the diagonal of the rectangle will be the length of the handrail
We can use the Pythagorean Theorem to solve this
Handrail length = √ [ (4.5 pi)^2 + 10^2 ] ≈ 17.3 ft
Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
Learn more about the Pythagorean theorem here: brainly.com/question/343682
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