brentking2001
19.03.2020 •
Mathematics
A soft drink can is h centimeters tall and has a radius of r cm. The cost of material in the can is 0.0005 cents per cm2 and the soda itself costs 0.002 cents per cm3. The cans are currently 4 cm tall and have a radius of 4 cm. Use calculus to estimate the effect on costs of increasing the radius.
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Ответ:
Step-by-step explanation:
Given:
The cost of material in the can is 0.0005 cents per cm2 The soda itself costs 0.002 cents per cm3.1. The Volume of the can is: V = Sh = π h = 3.14* *4 = 200.96
2. The surface area of the can is
S = 2π + 2rhπ = 2*3.14* + 2*4*4*3.14
= 100.48 + 100.48
= 200.96
The total cost of the can is: 0.0005*200.96 + 0.002*200.96
If we increase the radius, the cost will be increased as well. Because the volume and the surface area will increase.
Ответ:
Step-by-step explanation:
Given:
Cost of material, Cm = 0.0005 cents per cm2
Cost of soda, Cs = 0.002 cents per cm3
Height, h = 4 cm
Radius, r = 4 cm
Surface area of a cylinder, Ac = 2πrh + 2πr^2
= 2π × 4 × (4 + 4)
= 64π cm^2
Volume of a cylinder, V = πr^2 × h
= π × (4^2) × 4
= 64π cm^3
dAs = dAs/dr ×dr + dAs/dh × dh
= 2πh + 4πr × dr + 2πr × dh
= 8π + 16π × dr + 8π × dh
= 24π dr + 8π dh
dr = 0.1 cm
dh = -0.8 cm
dAs = 2.4π - 6.4π
= -4π × 0.0005
Cost = -0.00628
dV = dV/dr ×dr + dV/dh × dh
= 2πrh× dr + πr^2 × dh
= 32π × dr + 16π × dh
dr = 0.1 cm
dh = -0.8 cm
dAs = 3.2π - 12.8π
= -9.6π × 0.002
Cost = -0.603
Total cost = -0.00628 - 0.603
= -0.609
Ответ: