To find the surface area of a cone, we first need to find the slant height. The slant height of a cone is the distance from the vertex to any point on the base edge. We can use the Pythagorean theorem to find the slant height.
In this case, the radius is 6, the hypotenuse (which is the slant height) is 11, and the height is unknown. We can use the Pythagorean theorem to find the height.
Using the Pythagorean theorem:
height^2 + radius^2 = slant height^2
height^2 + 6^2 = 11^2
height^2 + 36 = 121
height^2 = 85
height ≈ √85 ≈ 9.2
Now that we have the height, we can calculate the surface area of the cone.
The surface area of a cone is given by the formula:
surface area = πr(r + slant height)
Plugging in the values:
surface area = 3.14 * 6(6 + 11)
surface area = 3.14 * 6(17)
surface area ≈ 3.14 * 6 * 17 ≈ 322.14
Therefore, the surface area of the cone is approximately 322.14 square units.
A cone shows a radius of 6 and hypotenuse or side as 11.
What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.
(1 point)
5 answers
A cook wants to cover the side of a cone-shaped funnel with parchment paper to avoid any leaks or spills. The funnel has a diameter of 6 inches and a slant height of 4 inches. How many square inches of parchment paper is needed to cover the side of the funnel? Use 3.14 for pi and round your answer to the nearest hundredth.(1 point)
To find the surface area of the side of the funnel, we need to find the circumference of the base. The circumference of a circle is given by the formula: circumference = π*diameter.
Given that the diameter of the funnel is 6 inches, we can find the circumference:
circumference = 3.14 * 6 = 18.84 inches
Now we can calculate the surface area of the side of the funnel.
The surface area of a cone is given by the formula:
surface area = π * radius * slant height
In this case, the radius is half of the diameter, so it is 6/2 = 3 inches.
The slant height is given as 4 inches.
Plugging in the values, we get:
surface area = 3.14 * 3 * 4 = 37.68 square inches
Therefore, approximately 37.68 square inches of parchment paper are needed to cover the side of the funnel.
Given that the diameter of the funnel is 6 inches, we can find the circumference:
circumference = 3.14 * 6 = 18.84 inches
Now we can calculate the surface area of the side of the funnel.
The surface area of a cone is given by the formula:
surface area = π * radius * slant height
In this case, the radius is half of the diameter, so it is 6/2 = 3 inches.
The slant height is given as 4 inches.
Plugging in the values, we get:
surface area = 3.14 * 3 * 4 = 37.68 square inches
Therefore, approximately 37.68 square inches of parchment paper are needed to cover the side of the funnel.
A waffle cone is in the shape of a cone with a slant height of 8 inches and a radius of 3 inches. A baker wants to know the surface area of the cone in order to cover the cone with melted chocolate. What is the surface area of the side of the cone in square inches? Use 3.14 for pi and round your answer to the nearest hundredth.(1 point)
To find the surface area of the side of the cone, we need to calculate the lateral surface area. The lateral surface area of a cone is given by the formula: lateral surface area = π * radius * slant height.
Given that the radius is 3 inches and the slant height is 8 inches, we can calculate the lateral surface area:
lateral surface area = 3.14 * 3 * 8 = 75.36 square inches.
Therefore, the surface area of the side of the cone is approximately 75.36 square inches.
Given that the radius is 3 inches and the slant height is 8 inches, we can calculate the lateral surface area:
lateral surface area = 3.14 * 3 * 8 = 75.36 square inches.
Therefore, the surface area of the side of the cone is approximately 75.36 square inches.