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 = 2pi rh ).

Explanation:

Step1: Calculate lateral area of Silo A

The formula for lateral area \( LA = 2\pi rh \). For Silo A, \( r = 6 \) feet, \( h = 60 \) feet.
\( LA_A=2\pi\times6\times60 = 720\pi\) square feet. Cost \( C_A=1.2\times720\pi=864\pi\approx 2712.96\) dollars.

Step2: Calculate lateral area of Silo B

For Silo B, \( r = 8 \) feet, \( h = 50 \) feet.
\( LA_B=2\pi\times8\times50 = 800\pi\) square feet. Cost \( C_B=1.2\times800\pi = 960\pi\approx3014.4\) dollars.

Step3: Calculate lateral area of Silo C

For Silo C, \( r = 10 \) feet, \( h = 34 \) feet.
\( LA_C=2\pi\times10\times34=680\pi\) square feet. Cost \( C_C=1.2\times680\pi = 816\pi\approx2562.24\) dollars.

Step4: Calculate lateral area of Silo D

For Silo D, \( r = 12 \) feet, \( h = 20 \) feet.
\( LA_D=2\pi\times12\times20 = 480\pi\) square feet. Cost \( C_D=1.2\times480\pi=576\pi\approx 1808.64\) dollars.

Answer:

Silo D