Question

An advertisement for the state fair will be painted on one of four silos along the highway into town. The silos are in the shape of cylinders. Only the lateral area of the silo will be painted, not the top and bottom. If it costs $1.20 per square foot to paint the sides of the silo, which silo will cost the least to paint?
Recall the formula LA=2 pi rh.
A. Silo A
B. Silo B
C. Silo C
D. Silo D

Answer 1

Answer: Silo D

Step-by-step explanation:

i just took the test

Answer 2

Answer: Silo D

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How I got that answer:

r = radius

h = height

LA = lateral surface area of cylinder

LA = 2*pi*r*h

Let's find the lateral surface area of each silo. The smallest lateral surface area will lead to the lowest total cost.

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Silo A

LA = 2*pi*r*h

LA = 2*pi*6*60

LA = 720pi

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Silo B

LA = 2*pi*r*h

LA = 2*pi*8*50

LA = 800pi

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Silo C

LA = 2*pi*r*h

LA = 2*pi*10*34

LA = 680pi

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Silo D

LA = 2*pi*r*h

LA = 2*pi*12*20

LA = 480pi

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If we ignore the "pi" terms for each of the four answers above, we see that 480 is the smallest value. Silo D has the smallest lateral surface area at 480pi square feet.

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Side note: to determine the total cost, you multiply the surface area by the cost per square foot ($1.20)

For example, the total cost to paint silo D is

cost = (surface area)*(price per square foot)

cost = (480*pi)*(1.20)

cost = 1809.557

cost = 1809.56

This section is optional as your teacher isnt requiring you to find the actual costs, but rather just the silo with the least amount of area. You could go the longer route to find each surface area, compute the total cost, and then compare the total costs. You should find that silo D's cost is the lowest.