Find the volume of the figure: a prism of volume 15 with a pyramid of the same height cut out.
1 answer:
The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.
Step-by-step explanation:
The given is,
A prism of volume 15
A pyramid of the same height cut out
For the above question diagram is missing, so i attach the diagram.
Step:1
Ref the attachment,
Volume of figure = Volume of Prism - Volume of Pyramid....(1)
Step:2
From the given diagram,
Formula for volume of prism,
......................(2)
Where, w - Width of the prism
h - Height of prism
l - Length of prism
From the given,
Volume, V = 15 cubic units
l = a
w = b
h = c
Equation (1) becomes,
15 = abc
c =
Step:3
Volume of pyramid, ..........................(2)
where,
w - Width of pyramid
h - Height of pyramid
l - Length of pyramid
From the given,
l = a
w = b
h = c
From the volume of prism, h = c =
Equation (2) becomes,
= 5
cubic units
Step:4
Equation (1) becomes,
Volume of figure = 15 - 5
= 10 cubic units
Result:
The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.
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Answer:
Step-by-step explanation:
Part A
x-intercepts of the graph → x = 0, 6
Maximum value of the graph → f(x) = 120
Part B
Increasing in the interval → 0 ≤ x ≤ 3
Decreasing in the interval → 3 < x ≤ 6
As the price of goods increase in the interval [0, 3], profit increases.
But in the price interval of (3, 6] profit of the company decreases.
Part C
Average rate of change of a function 'f' in the interval of x = a and x = b is given by,
Average rate of change =
Therefore, average rate of change of the function in the interval x = 1 and x = 3 will be,
Average rate of change =
=
= 30