What is the formula for the total surface area of a cylinder?(1 point)

Question

2. Find the surface area of a cylinder with a radius of 4 cm and a height of 2 cm. Use the approximation of 3.14 for pi.(1 point)
___square centimeters

3. 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.(1 point)
in^2

4. 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.(1 point)

5. 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.(1 point)

Answer 1

1. The formula for the total surface area \( A \) of a cylinder is given by: \[ A = 2\pi r(h + r) \] where \( r \) is the radius and \( h \) is the height of the cylinder.

2. To find the surface area of a cylinder with a radius of 4 cm and a height of 2 cm using \( \pi \approx 3.14 \):

\[ A = 2\pi r(h + r) = 2 \times 3.14 \times 4(2 + 4) = 2 \times 3.14 \times 4 \times 6 \] \[ = 2 \times 3.14 \times 24 = 150.72 \] The surface area is approximately 150.7 square centimeters.

3. For a cylinder with a diameter of 12 inches, the radius \( r \) is half of the diameter: \[ r = \frac{12}{2} = 6 \text{ inches} \] The height \( h \) is 10 inches. Using the formula for surface area: \[ A = 2\pi r(h + r) = 2 \times 3.14 \times 6(10 + 6) = 2 \times 3.14 \times 6 \times 16 \] \[ = 2 \times 3.14 \times 96 = 602.88 \] The surface area is approximately 602.9 in².

4. The total surface area needed to cover the sides and top of a cylinder cake with a radius of 5 inches and a height of 7 inches is given by the lateral area of the side plus the area of the top:

\[ \text{Lateral Area} = 2\pi rh = 2 \times 3.14 \times 5 \times 7 \] \[ = 2 \times 3.14 \times 35 = 219.8 \] \[ \text{Area of the top} = \pi r^2 = 3.14 \times (5^2) = 3.14 \times 25 = 78.5 \] Adding these two areas together: \[ A = 219.8 + 78.5 = 298.3 \] So, the amount of icing needed is approximately 298.3 square inches.

5. For the silo with a radius of 4 feet and a height of 30 feet, only the lateral surface area needs to be calculated since the top and bottom are not being refinished: \[ \text{Lateral Area} = 2\pi rh = 2 \times 3.14 \times 4 \times 30 \] \[ = 2 \times 3.14 \times 120 = 752.8 \] So, the amount of aluminum needed is approximately 752.8 square feet.

Answer 2

why did you get EVERYTHING wrong?!?!

Answer 3

I apologize for any mistakes in my calculations. Let’s go through each question step-by-step to ensure accuracy.

1. Surface Area Formula: The correct formula for the total surface area \( A \) of a cylinder is: \[ A = 2\pi r(h + r) \] or alternatively, \[ A = 2\pi rh + 2\pi r^2 \] (where \( r \) is the radius and \( h \) is the height).

2. Surface Area of a Cylinder with Radius 4 cm and Height 2 cm: \[ A = 2\pi r(h + r) = 2 \times 3.14 \times 4(2 + 4) \] \[ = 2 \times 3.14 \times 4 \times 6 \] \[ = 2 \times 3.14 \times 24 = 150.72 \] The surface area is approximately 150.7 square centimeters.

3. Surface Area of a Cylinder with Diameter 12 inches (Radius 6 inches) and Height 10 inches: \[ A = 2\pi r(h + r) = 2 \times 3.14 \times 6 (10 + 6) \] \[ = 2 \times 3.14 \times 6 \times 16 \] \[ = 2 \times 3.14 \times 96 = 602.88 \] The surface area is approximately 602.9 square inches.

4. Surface Area of a Cylinder Cake with Radius 5 inches and Height 7 inches (Top and Sides Only):

   • Lateral Surface Area: \[ \text{Lateral Area} = 2\pi rh = 2 \times 3.14 \times 5 \times 7 \] \[ = 2 \times 3.14 \times 35 = 219.8 \]

   • Area of the Top: \[ \text{Area of the top} = \pi r^2 = 3.14 \times 25 = 78.5 \]

   Adding these two areas together: \[ A = 219.8 + 78.5 = 298.3 \] The amount of icing needed is approximately 298.3 square inches.

5. Surface Area of a Silo with Radius 4 feet and Height 30 feet (No Top or Bottom): \[ \text{Lateral Area} = 2\pi rh = 2 \times 3.14 \times 4 \times 30 \] \[ = 2 \times 3.14 \times 120 = 752.8 \] The amount of aluminum needed is approximately 752.8 square feet.

Please let me know specifically which part or calculation didn't seem correct, and I will be happy to clarify or correct it further!

Answer 4

you poo poo

1. 2πr^2 + 2πrh
2. 150.72
3. 602.88
4. 298.3
5. 753.6

Answer 5

I apologize for the oversight and any errors. Let's clarify the correct formula and calculations based on your feedback:

1. Surface Area Formula: The formula for the total surface area of a cylinder is indeed: \[ A = 2\pi r^2 + 2\pi rh \]

2. Surface Area of a Cylinder with Radius 4 cm and Height 2 cm: \[ A = 2\pi r^2 + 2\pi rh = 2\pi(4^2) + 2\pi(4)(2) \] \[ = 2\pi(16) + 2\pi(8) \] \[ = 32\pi + 16\pi = 48\pi \] Using \( \pi \approx 3.14 \): \[ 48 \times 3.14 = 150.72 , \text{cm}^2 \] Your calculation is correct: 150.72 square centimeters.

3. Surface Area of a Cylinder with Diameter 12 inches and Height 10 inches (Radius 6 inches): \[ A = 2\pi r^2 + 2\pi rh = 2\pi(6^2) + 2\pi(6)(10) \] \[ = 2\pi(36) + 2\pi(60) \] \[ = 72\pi + 120\pi = 192\pi \] Using \( \pi \approx 3.14 \): \[ 192 \times 3.14 = 602.88 , \text{in}^2 \] Your calculation is correct: 602.88 in².

4. Surface Area of a Cylinder Cake with Radius 5 inches and Height 7 inches (Sides and Top): \[ A = 2\pi r^2 + 2\pi rh \]

   • Lateral Area: \( 2\pi rh \) \[ = 2\pi(5)(7) = 70\pi \]
   • Top Area: \( \pi r^2 \) \[ = \pi(5^2) = 25\pi \]

   Adding both: \[ Total = 70\pi + 25\pi = 95\pi \] Using \( \pi \approx 3.14 \): \[ 95 \times 3.14 = 298.3 , \text{square inches} \] Your calculation is correct: 298.3 square inches.

5. Surface Area of a Silo with Radius 4 feet and Height 30 feet (No Top or Bottom): \[ A = 2\pi rh = 2\pi(4)(30) = 240\pi \] Using \( \pi \approx 3.14 \): \[ 240 \times 3.14 = 753.6 , \text{square feet} \] Your calculation is correct: 753.6 square feet.

Thank you for your patience, and I appreciate your corrections! If you have any further questions or need more assistance, feel free to ask!

Answer 6

QUICK CHECK.

1. Find the surface area of a cylinder with a radius of 5 inches and a height of 10 inches.
Answer: 471 square inches
2. Use the image to answer the question. A cylinder is labeled with a height of 8 yards and a radius of 7 yards. Find the surface area of the cylinder.
New Answer: 252.77 square yards
3. Use the image to answer the question. A cylinder is labeled with a height of 3 yards and a radius of 2 yards. Find the surface area of the cylinder.
New Answer: 25.12 square yards
4. A can of olives has a diameter of 6 inches and a height of 4 inches. How many square inches of paper will be needed for the label on the outside of the can?
Answer: 75.36 square inches
5. A wheel of cheese has a diameter of 6 inches and a height of 2 inches. A chef is making an appetizer where the cheese will be covered with pastry. To know how much pastry is needed, the chef wants to know the surface area of the cheese wheel. What is the total surface area of the cheese wheel in square inches?
Answer: 94.2 square inches

Answer 7

Let's verify each calculation step by step.

1. Surface Area of a Cylinder with Radius 5 inches and Height 10 inches:

   • Using the formula \( A = 2\pi r^2 + 2\pi rh \): \[ A = 2\pi(5^2) + 2\pi(5)(10) = 2\pi(25) + 2\pi(50) = 50\pi + 100\pi = 150\pi \] Using \( \pi \approx 3.14 \): \[ A \approx 150 \times 3.14 = 471 \text{ square inches} \] Your answer is correct: 471 square inches.

2. Surface Area of a Cylinder with Height 8 yards and Radius 7 yards:

   • Again using the formula: \[ A = 2\pi(7^2) + 2\pi(7)(8) \] \[ = 2\pi(49) + 2\pi(56) = 98\pi + 112\pi = 210\pi \] Using \( \pi \approx 3.14 \): \[ A \approx 210 \times 3.14 = 659.4 \text{ square yards} \] If you're referring to a different value or context for the dimensions, please verify the stated dimensions.

3. Surface Area of a Cylinder with Height 3 yards and Radius 2 yards:

   • Using the formula: \[ A = 2\pi(2^2) + 2\pi(2)(3) \] \[ = 2\pi(4) + 2\pi(6) = 8\pi + 12\pi = 20\pi \] Using \( \pi \approx 3.14 \): \[ A \approx 20 \times 3.14 = 62.8 \text{ square yards} \] This seems to differ from your answer of 25.12 square yards.

4. Surface Area of a Can of Olives (Diameter 6 inches, Height 4 inches):

   • Radius is \( r = \frac{6}{2} = 3 \) inches.
   • Using the formula: \[ A = 2\pi(3^2) + 2\pi(3)(4) \] \[ = 2\pi(9) + 2\pi(12) = 18\pi + 24\pi = 42\pi \] Using \( \pi \approx 3.14 \): \[ A \approx 42 \times 3.14 = 131.88 \text{ square inches} \] This differs from the stated answer of 75.36 square inches.

5. Surface Area of a Wheel of Cheese (Diameter 6 inches, Height 2 inches):

   • Radius is \( r = \frac{6}{2} = 3 \) inches.
   • Using the formula: \[ A = 2\pi(3^2) + 2\pi(3)(2) \] \[ = 2\pi(9) + 2\pi(6) = 18\pi + 12\pi = 30\pi \] Using \( \pi \approx 3.14 \): \[ A \approx 30 \times 3.14 = 94.2 \text{ square inches} \] Your answer is correct: 94.2 square inches.

Summary of Results:

1. Correct: 471 square inches
2. Not matching, should be: 659.4 square yards
3. Not matching, should be: 62.8 square yards
4. Not matching, should be: 131.88 square inches
5. Correct: 94.2 square inches

If you have specific images or contexts for the cylinders that might change these numbers, please share and I can adjust accordingly!