what is the first area in square meters of a cone with a slant height of 8 m and a radius of 5 m used 3.14 for pi. round to the nearest tenth if necessary
To find the surface area of a cone, we need to calculate the lateral surface area and then add it to the base area.
The lateral surface area of a cone is given by the formula: A = π * r * s, where A represents the lateral surface area, r represents the radius of the cone, and s represents the slant height of the cone.
Given that the radius (r) is 5 m and the slant height (s) is 8 m, we can substitute these values into the formula:
A = 3.14 * 5 * 8
Simplifying this expression, we get:
A ≈ 125.6 square meters
To find the complete surface area, we need to add the base area. The base area of a cone is given by the formula: A = π * r^2, where r represents the radius of the cone.
Substituting the radius (r = 5 m) into the formula, we have:
A = 3.14 * (5)^2
Simplifying this expression, we get:
A = 3.14 * 25
A ≈ 78.5 square meters
To get the total surface area, we add the lateral surface area and the base area:
Total surface area ≈ 125.6 + 78.5 = 204.1 square meters
Therefore, the first area, rounded to the nearest tenth, is approximately 204.1 square meters.
what is the surface area in square feet of a cone with a diameter of 12ft and a slant height of 14ft use 3.14 for pi.round to the nearest tenth if necessary
what is the surface area in square centimeters of a cone with a diameter of 12 ft and a slant height of 14 ft use 3.14 for pi. round to the nearest tenth if necessary.
To find the surface area of a cone, let's first convert the given diameter and slant height from feet to centimeters. Keep in mind that 1 foot is equal to 30.48 centimeters.
Given the diameter is 12 ft, it is equal to 12 * 30.48 = 365.76 cm.
Given the slant height is 14 ft, it is equal to 14 * 30.48 = 426.72 cm.
Next, we will calculate the radius using the diameter given. The radius (r) is half the diameter.
Given the diameter in centimeters (d = 365.76 cm), the radius (r) is 365.76 cm / 2 = 182.88 cm.
Now, let's find the lateral surface area of the cone. It is given by the formula: A = π * r * s, where A represents the lateral surface area, r represents the radius, and s represents the slant height.
Substituting the values we have in centimeters, we get:
A = 3.14 * 182.88 cm * 426.72 cm
Simplifying this expression, we have:
A ≈ 247,280.9856 square centimeters
To find the total surface area, we need to add the base area. The base area of a cone is given by the formula: A = π * r^2, where r represents the radius.
Substituting the radius (r = 182.88 cm) into the formula, we have:
A = 3.14 * (182.88 cm)^2
Simplifying this expression, we have:
A = 3.14 * 33445.3344 cm^2
A ≈ 104,987.942016 square centimeters
To get the total surface area, we add the lateral surface area and the base area:
Total surface area ≈ 247,280.9856 + 104,987.942016 = 352,268.927616 square centimeters
Therefore, the surface area, rounded to the nearest tenth, is approximately 352,268.9 square centimeters.
incorrect
Apologies for the error. Let's recalculate the surface area of the cone correctly.
Given:
Diameter = 12 ft
Slant height = 14 ft
To find the radius (r) of the cone, divide the diameter by 2:
r = 12 ft / 2 = 6 ft
Next, convert the measurements from feet to centimeters. Since 1 foot is equal to 30.48 centimeters:
Diameter = 12 ft * 30.48 cm/ft = 365.76 cm
Slant height = 14 ft * 30.48 cm/ft = 426.72 cm
Radius = 6 ft * 30.48 cm/ft = 182.88 cm
Now we can find the lateral surface area by using the formula: A = π * r * s, where A represents the lateral surface area, r represents the radius, and s represents the slant height.
A = 3.14 * 182.88 cm * 426.72 cm
Simplifying this expression, we get:
A ≈ 245,087.5264 square centimeters
To find the total surface area, we need to add the base area. The base area of a cone is given by the formula: A = π * r^2, where r represents the radius.
A = 3.14 * (182.88 cm)^2
Simplifying this expression, we get:
A ≈ 104,671.8759 square centimeters
To get the total surface area, we add the lateral surface area and the base area:
Total surface area ≈ 245,087.5264 + 104,671.8759 = 349,759.4023 square centimeters
Therefore, the surface area, rounded to the nearest tenth, is approximately 349,759.4 square centimeters.
ok just dont round it
Apologies for the confusion. Without rounding, the surface area of the cone is approximately 349,759.4023 square centimeters.
a cone has a radius of 6 with a height of 11 what is the surface area of the cone use 3.14 for pi and round to the nearest tenth if necessary
To find the surface area of a cone, we need to calculate the lateral surface area and add it to the base area.
The lateral surface area of a cone is given by the formula: A = π * r * s, where A represents the lateral surface area, r represents the radius of the cone, and s represents the slant height of the cone.
Given that the radius (r) is 6 and the height (h) is 11, we can calculate the slant height (s) using the Pythagorean theorem. The slant height (s) is given by: s = sqrt(r^2 + h^2).
Substituting the values we have, we get:
s = sqrt(6^2 + 11^2)
s = sqrt(36 + 121)
s = sqrt(157)
s ≈ 12.52996
Now, we can calculate the lateral surface area:
A = 3.14 * 6 * 12.52996
A ≈ 235.619
To find the base area, we can use the formula for the area of a circle:
A = π * r^2
Substituting the radius (r = 6) into the formula, we get:
A = 3.14 * 6^2
A = 3.14 * 36
A ≈ 113.04
To find the total surface area, we add the lateral surface area and the base area:
Total surface area ≈ 235.619 + 113.04
Total surface area ≈ 348.659
Therefore, the surface area of the cone is approximately 348.7 square units when rounded to the nearest tenth.