Which pyramid has a greater volume, and how much greater is its volume? A rectangular pyramid on the left with a base of 7 inche
1 answer:
Answer:
Which pyramid has a greater volume? the first pyramid (left pyramid) with a volume of
How much greater is its volume? its volume is greater than the second (right) pyramid
Step-by-step explanation:
Equation to find the volume of a pyramid:
where is the area of the base, and
is the height.
- First pyramid:
length:
width:
height:
Area of the rectangular base:
Volume of the first pyramid:
- Second pyramid:
length:
width:
height:
Area of the rectangular base:
Volume of the second pyramid:
Which pyramid has a greater volume? the first pyramid (left pyramid) with a volume of
How much greater is its volume? its volume is greater than the second (right) pyramid
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Take the derivative with respect to t
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
divide by w
we add sin(wt) to both sides
divide both sides by cos(wt)
OR
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be
since 2npi is just the period of cos
substituting our second soultion we get
since 2npi is the period
so the maximum value =
minimum value =
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
divide by w
we add sin(wt) to both sides
divide both sides by cos(wt)
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be
since 2npi is just the period of cos
substituting our second soultion we get
since 2npi is the period
so the maximum value =
minimum value =