Find the surface area of the cylinder. Use the approximation of 3.14 for pi.
the circle is 2 yd and the face is 3 yd
To find the surface area of the cylinder, we need to find the area of the two circular bases and the lateral surface area.
Area of the circular bases:
The formula to find the area of a circle is A = πr², where A is the area and r is the radius.
Given that the radius of the circle is 2 yards, the area of one circular base is A₁ = π(2)² = 4π square yards.
The cylinder has two circular bases, so the total area of both bases is 2A₁ = 2(4π) = 8π square yards.
Lateral surface area:
The lateral surface area of a cylinder is given by the formula L = 2πrh, where L is the lateral surface area, r is the radius, and h is the height.
Given that the height of the cylinder is 3 yards, the lateral surface area is L = 2π(2)(3) = 12π square yards.
Total surface area:
To find the total surface area, we add the area of the two circular bases and the lateral surface area:
Total surface area = 8π + 12π = 20π square yards.
Using the approximation of π as 3.14, the surface area of the cylinder is approximately 20(3.14) = 62.8 square yards.
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? Use 3.14 for pi.
To find the surface area of the can that needs to be covered by the label, we need to find the area of the curved surface (excluding the top and bottom).
Curved Surface Area:
The formula to find the surface area of a cylinder is A = 2πrh, where A is the surface area, r is the radius, and h is the height.
Given that the diameter of the can is 6 inches, the radius is 6/2 = 3 inches.
Given that the height of the can is 4 inches, the surface area of the curved surface is A = 2π(3)(4) = 24π square inches.
Using the approximation of π as 3.14, the surface area of the curved surface is approximately 24(3.14) = 75.36 square inches.
Therefore, approximately 75.36 square inches of paper will be needed for the label on the outside of the can.
A wheel of cheese has a diameter of 6 inches and a height of 2 inch. 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? Use 3.14 for pi.
To find the total surface area of the cheese wheel, we need to find the area of the curved side and the area of the two circular ends.
Curved Surface Area:
The formula to find the surface area of a cylinder is A = 2πrh, where A is the surface area, r is the radius, and h is the height.
Given that the diameter of the cheese wheel is 6 inches, the radius is 6/2 = 3 inches.
Given that the height of the cheese wheel is 2 inches, the curved surface area is A = 2π(3)(2) = 12π square inches.
Circular End Areas:
The formula to find the area of a circle is A = πr², where A is the area and r is the radius.
Given that the radius of the cheese wheel is 3 inches, the area of each circular end is A = π(3)² = 9π square inches.
Since there are two circular ends, their total area is 2(9π) = 18π square inches.
Total Surface Area:
To find the total surface area, we add the curved surface area to the sum of the circular end areas:
Total surface area = 12π + 18π = 30π square inches.
Using the approximation of π as 3.14, the total surface area of the cheese wheel is approximately 30(3.14) = 94.2 square inches.
What is the formula for the total surface area of a cylinder?
The formula for the total surface area of a cylinder is:
A = 2πr² + 2πrh,
where A is the total surface area, r is the radius of the base, and h is the height of the cylinder.
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.
To find the surface area of the cylinder, we need to use the formula:
A = 2πr² + 2πrh.
Given that the radius is 4 cm and the height is 2 cm, we can substitute these values into the formula:
A = 2(3.14)(4²) + 2(3.14)(4)(2).
A = 2(3.14)(16) + 2(3.14)(4)(2).
A = 2(3.14)(16) + 2(3.14)(8).
A = 100.48 + 50.24.
A ≈ 150.72 square centimeters.