Answer:
x=27
Step-by-step explanation:
In order to solve for the variable, x, let us first expand the left side to get rid of the parenthesis:
Now, let us get all the variables of x on one side, and all the numerical values on the other in order to <u>isolate the variable</u>, x.
<em>I hope this helps! Please let me know if you have any further questions :)</em>
area=(b1+b2)*h all divided by 2
a=(12+12+8.7)*4.9 all divided by 2
a=32.7*4.9/2
a=160.23/2
a=80.12 sq. ft.
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>
