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.(1 point)
Responses
131.88
131.88
75.36
75.36
150.72
150.72
376.8
To find the surface area of the cylinder (which represents the label on the outside of the can), we need to find the area of the curved surface (lateral surface area) and the area of the circular top and bottom.
The formula for the lateral surface area of a cylinder is LSA = 2πrh, where r is the radius and h is the height.
The formula for the area of a circle is A = πr^2.
Given that the diameter of the can is 6 inches, the radius (r) is half of that, which is 6/2 = 3 inches.
The lateral surface area is LSA = 2π(3)(4) = 24π square inches.
The area of each circular top and bottom is A = π(3)^2 = 9π square inches.
Therefore, the total surface area of the cylinder is 24π + 9π + 9π = 42π square inches.
Using 3.14 for π, we can calculate the numerical value:
42π = 42 × 3.14 = 131.88 square inches.
So, the correct answer is 131.88 square inches.
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.(1 point)
Responses
37.68 square inches
37.68 square inches
94.2 square inches
94.2 square inches
301.44 square inches
301.44 square inches
62.8 square inches
To find the surface area of the cheese wheel, we need to find the area of the curved surface (lateral surface area) and the area of the circular top and bottom.
The formula for the lateral surface area of a cylinder is LSA = 2πrh, where r is the radius and h is the height.
The formula for the area of a circle is A = πr^2.
Given that the diameter of the cheese wheel is 6 inches, the radius (r) is half of that, which is 6/2 = 3 inches.
The lateral surface area is LSA = 2π(3)(2) = 12π square inches.
The area of each circular top and bottom is A = π(3)^2 = 9π square inches.
Therefore, the total surface area of the cheese wheel is 12π + 9π + 9π = 30π square inches.
Using 3.14 for π, we can calculate the numerical value:
30π = 30 × 3.14 = 94.2 square inches.
So, the correct answer is 94.2 square inches.
A cylinder has a height of 15 feet and a radius of 4 feet. Solve for the total surface area of the cylinder. Use 3.14 for π and round to the nearest tenth.(1 point)
Responses
60 feet2
60 feet squared
56.52 feet2
188.4 feet squared
301.44 feet2
100.48 feet squared
477.3 feet2
To find the total surface area of the cylinder, we need to find the area of the curved surface (lateral surface area) and the area of the circular top and bottom.
The formula for the lateral surface area of a cylinder is LSA = 2πrh, where r is the radius and h is the height.
The formula for the area of a circle is A = πr^2.
Given that the radius is 4 feet and the height is 15 feet:
The lateral surface area is LSA = 2π(4)(15) = 120π square feet.
The area of each circular top and bottom is A = π(4)^2 = 16π square feet.
Therefore, the total surface area of the cylinder is 120π + 16π + 16π = 152π square feet.
Using 3.14 for π, we can calculate the numerical value:
152π = 152 × 3.14 ≈ 477.3 square feet.
So, the correct answer is 477.3 square feet, rounded to the nearest tenth.
what's the surface area of a cylinder. Use the approximation of 3.14 for pi.
(1 point)
Responses
32.97
32.97
75.36
75.36
25.12
25.12
62.8
The surface area of a cylinder can be found by adding the areas of the two circular bases and the lateral surface area.
The formula for the lateral surface area of a cylinder is LSA = 2πrh, where r is the radius and h is the height.
The formula for the area of a circle is A = πr^2.
Given that we have an approximate value for π of 3.14, we can calculate the surface area using the provided radius and height.
First, we'll calculate the lateral surface area:
LSA = 2πrh = 2(3.14)(r)(h) = 6.28rh square units.
Next, we'll calculate the area of the circular bases:
A = πr^2 = 3.14(r^2) square units.
To find the total surface area, we add the lateral surface area and the areas of the two circular bases:
Total surface area = LSA + 2A = 6.28rh + 2(3.14)(r^2) square units.
Without specific values for the radius and height, we can't calculate the exact surface area. Therefore, none of the provided options (32.97, 75.36, 25.12, or 62.8) can be determined as the correct answer.
So which is the answer
Apologies for the misunderstanding. To calculate the surface area of a cylinder, you need to add the areas of the two circular bases and the lateral surface area.
The formula for the lateral surface area of a cylinder is LSA = 2πrh, where r is the radius and h is the height.
The formula for the area of a circle is A = πr^2.
Given that you have an approximate value of 3.14 for π, we can calculate the surface area using the provided radius and height.
First, calculate the lateral surface area:
LSA = 2πrh = 2(3.14)(4)(15) = 377.04 square units.
Next, calculate the area of the circular bases:
A = πr^2 = 3.14(4^2) = 50.24 square units.
To find the total surface area, add the areas of the two circular bases and the lateral surface area:
Total surface area = LSA + 2A = 377.04 + 2(50.24) = 477.52 square units.
Rounding to the nearest tenth, the correct answer is 477.5 square units.