Answer: Second option.
Step-by-step explanation:
You need to use the following formula:
Where "B" is the area of its base and "h" is the height.
According to the data given in the exercise, you know that:
Therefore, knowing this values, you can substitute them into the formula shown before and then evaluate, in order to calculate the volume of thi right pyramid whose base is a regular hexagon.
Then, you get:
Answer:
V = 1/6 cubic units
Step-by-step explanation:
Applying the concept of integrals for volume calculation:
(1)
V = volume of the solid bounded by x = a and x = b
S(x) = cross section area of the solid, perpendicular to the x axis
From the figure we have that S is the area of a triangle that has base Z and height Y
Area of the triangle = (2)
Calculation of y(x) and z(x)
We apply the equation of the point-slope line (plane xy):
Slope = (3)
Equation of the line = (4)
Replacing the points (1,0) and (0,1) in (3):
Replacing the point (1,0) and m = -1 in (4):
y(x) = -x + 1 (Line A-B) (5)
We apply the equation of the point-slope line (plane xz):
Slope = (6)
Equation of the line = (7)
Replacing the points (1,0) and (0,1) in (6):
Replacing the point (1,0) and m = -1 in (7):
z(x) = -x + 1 (Line A-C) (8)
Replacing (5) and (8) in (2)
(9)
Replacing (9) in (1) and knowing that a = 0 and b = 1:
evaluated from x=0 to x=1
