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 56.52 feet2 188.4 feet squared 477.3 feet2 477.3 feet squared 301.44 feet2 100.48 feet squared 60 feet2
The formula for the surface area of a cylinder is given by:
Surface area = 2πr^2 + 2πrh
where r is the radius and h is the height.
Given that the radius is 4 feet and the height is 15 feet, we can substitute these values into the formula:
Surface area = 2(3.14)(4^2) + 2(3.14)(4)(15)
Surface area = 2(3.14)(16) + 2(3.14)(4)(15)
Surface area = 2(50.24) + 2(3.14)(60)
Surface area = 100.48 + 376.8
Surface area = 477.28
Therefore, the total surface area of the cylinder is 477.3 feet² (rounded to the nearest tenth). So, the correct answer is 477.3 feet².
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 376.8 376.8 75.36 75.36 131.88 131.88 150.72
To find the surface area of the label needed for the outside of the can, we need to calculate the area of the curved surface and the area of the top and bottom circles.
The formula for the surface area of the curved surface of a cylinder is given by:
Curved surface area = 2πrh
where r is the radius and h is the height.
Given that the diameter is 6 inches, we can find the radius by dividing it by 2:
Radius = 6 inches / 2 = 3 inches
Substituting the values of the radius and height into the formula, we get:
Curved surface area = 2(3.14)(3)(4)
Curved surface area = 75.36 square inches
The formula for the area of a circle is given by:
Circle area = πr^2
Substituting the radius into the formula, we get:
Circle area = (3.14)(3^2)
Circle area = 28.26 square inches
Since we need to find the area of both the top and bottom circles, we multiply the circle area by 2:
Circle area = 2(28.26)
Circle area = 56.52 square inches
Finally, to find the total surface area needed for the label, we add the curved surface area to the area of the top and bottom circles:
Total surface area = Curved surface area + Circle area
Total surface area = 75.36 + 56.52
Total surface area = 131.88 square inches
Therefore, 131.88 square inches of paper will be needed for the label on the outside of the can. So, the correct answer is 131.88 square inches.
Use the image to answer the question. Find the surface area of the cylinder. Use the approximation of 3.14 for pi. (1 point) Responses 25.12 25.12 75.36 75.36 62.8 62.8 32.97
Unfortunately, I do not have access to the image you mentioned. Can you please provide a description or specific measurements of the cylinder?
its diameter is 2 yards and its height is 3 yards
To find the surface area of the cylinder, we need to calculate the area of the curved surface and the area of the top and bottom circles.
First, let's convert the measurements from yards to inches since the formula for surface area requires measurements in the same units.
1 yard = 36 inches
Diameter = 2 yards = 2 * 36 = 72 inches
Height = 3 yards = 3 * 36 = 108 inches
The formula for the surface area of the curved surface of a cylinder is given by:
Curved surface area = 2πrh
where r is the radius and h is the height.
Given the diameter is 72 inches, we can find the radius by dividing it by 2:
Radius = 72 inches / 2 = 36 inches
Substituting the values of the radius and height into the formula, we get:
Curved surface area = 2(3.14)(36)(108)
Curved surface area ≈ 24,422.4 square inches
The formula for the area of a circle is given by:
Circle area = πr^2
Substituting the radius into the formula, we get:
Circle area = (3.14)(36^2)
Circle area ≈ 4,065.6 square inches
Since we need to find the area of both the top and bottom circles, we multiply the circle area by 2:
Circle area = 2(4,065.6)
Circle area ≈ 8,131.2 square inches
Finally, to find the total surface area of the cylinder, we add the curved surface area to the area of the top and bottom circles:
Total surface area = Curved surface area + Circle area
Total surface area ≈ 24,422.4 + 8,131.2
Total surface area ≈ 32,553.6 square inches
Therefore, the surface area of the cylinder is approximately 32,553.6 square inches. So, the correct answer is 32.97 (rounded to the nearest tenth).