The formula for volume of cone is:
V = π
r^2 h / 3
or
π r^2
h / 3 = 36 cm^3
Simplfying in terms of r:
r^2 = 108 / π h
To find for the smallest amount of paper that can create
this cone, we call for the formula for the surface area of cone:
S = π
r sqrt (h^2 + r^2)
S = π
sqrt(108 / π h) * sqrt(h^2 + 108 / π h)
S = π sqrt(108 / π h) * sqrt[(π h^3 + 108) / π h]
Surface area = sqrt (108) * sqrt[(π h + 108
/ h^2)]
<span>Getting the 1st derivative dS / dh then
equating to 0 to get the maxima value:</span>
dS/dh = sqrt (108) ((π – 216
/ h^3) * [(π h + 108/h^2)^-1/2]
Let dS/dh = 0 so,
π – 216
/ h^3 = 0
h^3 = 216 / π
h = 4.10
cm
Calculating
for r:
r^2 = 108 / π (4.10)
r = 2.90 cm
Answers:
h = 4.10 cm
<span>r = 2.90 cm</span>
Answer:
Part 1) Greta's right, the triangle is incorrect.
Part 2) 
Part 3) The height of the tree is 
, Trey’s house is not at risk
Step-by-step explanation:
Part 1) we know that
In the right triangle of the figure
Compare
therefore
The triangle is not correct
Because
The side adjacent to the 30 degree angle should be 
and the side opposite the 30 degree angle should be 
Part 2)
Let
x--------> the distance from the airplane to the SCCA (hypotenuse of the right triangle)
we know that
Part 3)
Let
x--------> the height of the tree
we know that
therefore
Trey’s house is not at risk
Answer:
i don't know what the math is. i would like to try to help
Step-by-step explanation:
