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.
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
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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.
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.
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.
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.
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.
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.
To find the surface area of the cylinder, we need to find the area of the two circular bases and the lateral surface area.
The formula for the 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.
Given that the diameter of the cylinder is 12 inches, we can find the radius by dividing the diameter by 2:
r = 12 / 2 = 6 inches.
The height of the cylinder is given as 10 inches.
Plugging these values into the formula, we have:
A = 2(3.14)(6²) + 2(3.14)(6)(10).
A = 2(3.14)(36) + 2(3.14)(6)(10).
A = 226.08 + 376.8.
A ≈ 602.88 square inches.
Therefore, the surface area of the cylinder is approximately 602.88 square inches.
The formula for the 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.
Given that the diameter of the cylinder is 12 inches, we can find the radius by dividing the diameter by 2:
r = 12 / 2 = 6 inches.
The height of the cylinder is given as 10 inches.
Plugging these values into the formula, we have:
A = 2(3.14)(6²) + 2(3.14)(6)(10).
A = 2(3.14)(36) + 2(3.14)(6)(10).
A = 226.08 + 376.8.
A ≈ 602.88 square inches.
Therefore, the surface area of the cylinder is approximately 602.88 square inches.
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.
To find the surface area of the sides and top of the cake that need to be covered with icing, we need to find the area of the curved surface and the area of the top.
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 radius of the cake is 5 inches and the height is 7 inches, the curved surface area is A = 2π(5)(7) = 70π square inches.
Top Area:
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 cake is 5 inches, the area of the top is A = π(5)² = 25π square inches.
Total Surface Area:
To find the total surface area, we add the curved surface area and the area of the top:
Total surface area = 70π + 25π = 95π square inches.
Using the approximation of π as 3.14, the total surface area of the sides and top of the cake is approximately 95(3.14) = 298.3 square inches.
Therefore, approximately 298.3 square inches of icing will be needed to cover the sides and top of the cake.
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 radius of the cake is 5 inches and the height is 7 inches, the curved surface area is A = 2π(5)(7) = 70π square inches.
Top Area:
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 cake is 5 inches, the area of the top is A = π(5)² = 25π square inches.
Total Surface Area:
To find the total surface area, we add the curved surface area and the area of the top:
Total surface area = 70π + 25π = 95π square inches.
Using the approximation of π as 3.14, the total surface area of the sides and top of the cake is approximately 95(3.14) = 298.3 square inches.
Therefore, approximately 298.3 square inches of icing will be needed to cover the sides and top of the cake.
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
To find the surface area of the sides of the silo that need to be refinished with aluminum, we need to find the area of the curved surface.
The formula for the surface area of a cylinder is:
A = 2πrh,
where A is the surface area, r is the radius of the base, and h is the height of the cylinder.
Given that the radius of the silo is 4 feet and the height is 30 feet, we can substitute these values into the formula:
A = 2(3.14)(4)(30).
A = 2(3.14)(120).
A ≈ 753.6 square feet.
Therefore, the farmer needs approximately 753.6 square feet of aluminum to refinish the sides of the silo.
The formula for the surface area of a cylinder is:
A = 2πrh,
where A is the surface area, r is the radius of the base, and h is the height of the cylinder.
Given that the radius of the silo is 4 feet and the height is 30 feet, we can substitute these values into the formula:
A = 2(3.14)(4)(30).
A = 2(3.14)(120).
A ≈ 753.6 square feet.
Therefore, the farmer needs approximately 753.6 square feet of aluminum to refinish the sides of the silo.
1 answer