What's the surface area?
1 answer:
Step-by-step Answer:
The given pyramid has a hexagonal (6-sides) base, which has the property that it is made up of six equilateral triangles each with side 8cm (same as the external side).
The apothem of each equilateral triangle is equal to sqrt(3)/2 of the side, namely 8sqrt(3)/2 = 4sqrt(3).
So area of the base is six times that of each equilateral triangle, whose individual area is given by A=base*height/2. So
area of equilateral triangle = (8) * 4sqrt(3) / 2 = 27.713
Area of base (6 equilateral triangles = 6*27.713
= 166.277 cm^2
To find the area of each slanted face, we need to calculate the apothem of each face, namely by using Pythagoras (see attached figure, on top left).
Apothem = sqrt(11^2+(4*sqrt(3))^2) = sqrt(121+48) = sqrt(169) = 13
Area of each slanted face = base * height (apothem) /2 = 8*13/2= 52
Area of six slanted faces = 6 * 52 = 312 cm^2
Total surface area = area of base + area of slanted faces
= 166.277 + 312
= 478.28 cm^2 (to hundredth cm^2)
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We are given that Commercial aircraft used for flying in instrument conditions are required to have two independent radios instead of one.
The probability of failure of one radio = 0.0026
So, the probability of failure of both radio =
Now we are supposed to find the probability that a particular flight will be safe with at least one working radio
A) the probability that a particular flight will be safe with at least one working radio = 1- 0.00000676=0.99999324
B)The usual rounding rule of three significant digits not work here because usual rounding rule of three significant digits makes it 1 which means that both radios are working properly.
C)Yes,this probability is high enough to ensure flight safety because it is close to 1