Here are the answers to your questions regarding the surface area of cylinders:
Q1: What is the formula for the total surface area of a cylinder?
- Answer: The formula for the total surface area \( A \) of a cylinder is: \[ A = 2\pi r(h + r) \] Where \( r \) is the radius and \( h \) is the height.
Q2: 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.
- Calculation: \[ A = 2\pi r(h + r) = 2 \times 3.14 \times 4(2 + 4) \] \[ A = 2 \times 3.14 \times 4 \times 6 = 2 \times 3.14 \times 24 = 150.72 , \text{cm}^2 \]
- Answer: The surface area is approximately 150.7 cm² (rounded to one decimal place).
Q3: Find the surface area of a cylinder with a diameter of 12 inches and a height of 10 inches. Use the approximation of 3.14 for pi.
- First, find the radius:
- Radius \( r = \frac{diameter}{2} = \frac{12}{2} = 6 \) inches.
- Calculation: \[ A = 2\pi r(h + r) = 2 \times 3.14 \times 6(10 + 6) \] \[ A = 2 \times 3.14 \times 6 \times 16 = 2 \times 3.14 \times 96 = 603.84 , \text{in}^2 \]
- Answer: The surface area is approximately 603.8 in² (rounded to one decimal place).
Q4: 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.
- Calculation:
- Surface area excluding the bottom: \[ A = \pi r^2 + 2\pi rh \] Where \( \pi r^2 \) is the area of the top and \( 2\pi rh \) is the area of the sides. \[ A = 3.14 \times 5^2 + 2 \times 3.14 \times 5 \times 7 \] \[ A = 3.14 \times 25 + 2 \times 3.14 \times 35 \] \[ A = 78.5 + 219.8 = 298.3 , \text{in}^2 \]
- Answer: The baker will need approximately 298.3 in² of icing (rounded to one decimal place).
Q5: 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.
- Calculation: \[ A = 2\pi rh \] \[ A = 2 \times 3.14 \times 4 \times 30 = 2 \times 3.14 \times 120 \] \[ A = 2 \times 376.8 = 753.6 , \text{ft}^2 \]
- Answer: The farmer needs approximately 753.6 ft² of aluminum (rounded to one decimal place).