Find the surface area of a cylinder with a diameter of 12 inches and height of 10 inches. Use the approximation of 3.14 for pi. Correct answer please

Answer 1

To find the surface area of a cylinder, you can use the formula:

\[ \text{Surface Area} = 2\pi r(h + r) \]

where:

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

Given:

• The diameter of the cylinder is 12 inches, so the radius \( r = \frac{12}{2} = 6 \) inches.
• The height \( h = 10 \) inches.
• Use \( \pi \approx 3.14 \).

Now, plug in the values into the formula:

1. Calculate \( h + r \): \[ h + r = 10 + 6 = 16 \]

2. Substitute \( r \) and \( h + r \) into the surface area formula: \[ \text{Surface Area} = 2 \cdot 3.14 \cdot 6 \cdot 16 \]

3. Calculate: \[ \text{Surface Area} = 2 \cdot 3.14 \cdot 6 \cdot 16 = 2 \cdot 3.14 \cdot 96 \] \[ = 6.28 \cdot 96 \] \[ = 602.88 \]

So, the surface area of the cylinder is approximately 602.88 square inches.

Answer 2

A baker needs to cover a cylinder cake with icing. The cake has a radius of 5 inches and a height of 7 inches. How many square inches of icing will be needed to cover the sides and top of the cake? Icing will not be added to the bottom of the cake. Use 3.14 for pi and round your answer to the nearest tenth.

Answer 3

To find the amount of icing needed to cover the sides and top of a cylindrical cake (excluding the bottom), we can calculate the surface area of the sides and the top of the cylinder using the formula for the surface area of a cylinder.

The surface area \(A\) we need can be calculated as follows:

\[ A = \text{Lateral Surface Area} + \text{Area of the Top} \]

1. Lateral Surface Area of the cylinder: \[ \text{Lateral Surface Area} = 2\pi rh \] where:

   • \(r\) is the radius,
   • \(h\) is the height.

2. Area of the Top of the cylinder: \[ \text{Area of the Top} = \pi r^2 \]

Given:

• \(r = 5\) inches,
• \(h = 7\) inches,
• Use \(\pi \approx 3.14\).

Calculate the Lateral Surface Area:

\[ \text{Lateral Surface Area} = 2 \cdot 3.14 \cdot 5 \cdot 7 \] \[ = 2 \cdot 3.14 \cdot 35 \] \[ = 6.28 \cdot 35 \] \[ = 219.8 , \text{square inches} \]

Calculate the Area of the Top:

\[ \text{Area of the Top} = 3.14 \cdot (5)^2 \] \[ = 3.14 \cdot 25 \] \[ = 78.5 , \text{square inches} \]

Total Area for Icing:

Now, add the lateral surface area and the top area to find the total area that needs to be covered with icing:

\[ A = \text{Lateral Surface Area} + \text{Area of the Top} \] \[ = 219.8 + 78.5 \] \[ = 298.3 , \text{square inches} \]

Final Answer:

The baker will need approximately 298.3 square inches of icing to cover the sides and top of the cake.

Answer 4

A 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.

Answer 5

To find the amount of aluminum needed to refinish the side of the silo, we only need to calculate the lateral surface area of the cylinder, as the farmer will not be refinishing the top or bottom of the silo.

The formula for the lateral surface area \(A\) of a cylinder is given by:

\[ A = 2\pi rh \]

where:

• \(r\) is the radius,
• \(h\) is the height.

Given:

• Radius \(r = 4\) feet
• Height \(h = 30\) feet
• Using \(\pi \approx 3.14\)

Calculate the Lateral Surface Area:

Substituting the known values into the formula:

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

1. Calculate \(2 \cdot 3.14\):

\[ 2 \cdot 3.14 = 6.28 \]

2. Now calculate \(6.28 \cdot 4\):

\[ 6.28 \cdot 4 = 25.12 \]

3. Finally, calculate \(25.12 \cdot 30\):

\[ 25.12 \cdot 30 = 753.6 \]

Final Answer:

The farmer needs approximately 753.6 square feet of aluminum to refinish the side of the silo.