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:42
Step-by-step explanation:
the " l l " on the -14 cancel out the negative
Answer:
<u>k = 1.5</u>
Step-by-step explanation:
To find the value of k, at first we will find the point of intersection of the lines
y =2x –5 and y = –x+1
Solve the equations to together by equating the values of y
So, 2x - 5 = -x + 1
Solve for x
3x = 6 ⇒ x = 6/3 = 2
So, y = -x + 1 = -2 + 1 = -1
So, the point of intersection of the lines ⇒ (2,-1)
line y = kx –4 pass through the point of intersection of the lines
so, line y = kx –4 pass through the point (2,-1)
So, at x = 2 , y = -1
∴ -1 = 2k - 4
Solve for k
-1 + 4 = 2k
2k = 3
k = 3/2 = 1.5
<u>So, the value of k is 1.5</u>
Answer:
14
Step-by-step explanation:
Because it occurs the most frequently in the given data set
If you're asking if 3/4 is less than 1/2, then it's a true statement.
