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:
r = 100 cm
Step-by-step explanation:
The radius is 1/2 of the diameter
1/2 d = 1/2(200) = 100
If you turn 9 1/3 in to a decimal and 3 1/2 in a decimal also
9 1/3 = 9.3 and 3 1/2 =3.5
9.3+3.5 =12.8
12.8=12 4/5
28(pi) is the same thing is (pi)(diameter)
so 28/2 is 14
14 is the radius
Answer: 1/3
Step-by-step explanation: The slope goes up 1 and over 3 each time. Rise over run : 1/3
