Question

A silo is a large cylinder container that holds hay and farmer needs to refinish the side is 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 trnth

Answer 1

To find the amount of aluminum needed to refinish the sides of the silo, we need to calculate the lateral surface area of the cylindrical 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.

Here, we are given:

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

Substituting these values into the formula:

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

Now let's calculate it step-by-step:

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

2. Calculate \( 6.28 \times 4 \): \[ 6.28 \times 4 = 25.12 \]

3. Finally, calculate \( 25.12 \times 30 \): \[ 25.12 \times 30 = 753.6 \]

Therefore, the total lateral surface area of the silo, and the amount of aluminum needed to refinish it, is:

\[ 753.6 \text{ square feet} \]

Rounding \( 753.6 \) to the nearest tenth gives us:

\[ \boxed{753.6} \text{ square feet} \]