Question

silo is a large cylinder container that holds hay. A farmer needs to refinish the side of the silo with aluminum. The silo has a radius of 4 feet and a height of 30 feet. How many square feet of aluminum does the farmer need to refinish the silo? He will not be refinishing the top or bottom of the silo. Use 3.14 for pi and round your answer to the nearest tenth.(1 point)

Answer 1

To find the surface area that the farmer needs to refinish, we need to calculate the lateral surface area of the cylinder (silo). The formula for the lateral surface area \( A \) of a cylinder is given by:

\[ A = 2 \pi r h \]

where:

• \( r \) is the radius of the cylinder,
• \( h \) is the height of the cylinder,
• \( \pi \) is approximately 3.14.

Given:

• Radius \( r = 4 \) feet,
• Height \( h = 30 \) feet.

Now we plug in the values into the formula:

\[ A = 2 \times 3.14 \times 4 \times 30 \]

Calculating this step by step:

1. Calculate \( 2 \times 3.14 \): \[ 2 \times 3.14 = 6.28 \]

2. Next, calculate \( 6.28 \times 4 \): \[ 6.28 \times 4 = 25.12 \]

3. Now, multiply \( 25.12 \) by \( 30 \): \[ 25.12 \times 30 = 753.6 \]

Thus, the lateral surface area of the silo is \( 753.6 \) square feet. Therefore, the farmer needs to refinish:

\[ \boxed{753.6} \]

square feet of aluminum.