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Ray Of Light [21]
3 years ago
7

A soup company wants to manufacture a can in the shape of a right circular cylinder that will hold 500 cm^3 of liquid. The mater

ial for the top and bottom costs 0.02 cent/cm^2, and the material for the sides costs 0.01 cent/cm^2.
a) Estimate the radius r and height h of the can that costs the least to manufacture. [suggestion: Express the cost C in terms of r.]
Physics
1 answer:
Rom4ik [11]3 years ago
4 0
The area of the top and bottom:
2πr²
Cost for top and bottom:
2πr²  x 0.02
= 0.04πr²

Area for side:
2πrh
Cost for side:
2πrh x 0.01
= 0.02πrh

Total cost:
C = 0.04πr² + 0.02πrh

We know that the volume of the can is:
V = πr²h
h = 500/πr²

Substituting this into the cost equation to get a cost function of radius:
C(r) = 0.04πr² + 0.02πr(500/πr²)
C(r) = 0.04πr² + 10/r

Now, we differentiate with respect to r and equate to 0 to obtain the minimum value:

0 = 0.08πr - 10/r²
10/r² = 0.08πr
r³ = 125/π

r = 3.41 cm
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2 years ago
When the mass of the bottle is 0.125 kg, the KE is______ kg m2/s2.
DiKsa [7]
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(1) KE = 1 kg m^2/s^2
(2) KE = 2 kg m^2/s^2
(3) KE = 3 kg m^2/s^2
(4) KE = 4 kg m^2/s^2


Explanation:

(1) Given mass = 0.125 kg
speed = 4 m/s

Since Kinetic energy = (1/2)*m*(v^2)

Plug in the values:
Hence:
KE = (1/2) * 0.125 * (16)
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(2) Given mass = 0.250 kg
speed = 4 m/s

Since Kinetic energy = (1/2)*m*(v^2)

Plug in the values:
Hence:
KE = (1/2) * 0.250 * (16)
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(3) Given mass = 0.375 kg
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Since Kinetic energy = (1/2)*m*(v^2)

Plug in the values:
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3 years ago
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