What is the surface area, in square centimeters, of a cone with a diameter of 12 feet and a slant height of 14 feet? Use 3.14 for pi and round to the nearest tenth, if necessary.(1 point)
Hey bot can you help me with this by giving the correct formula to figure out this problem??
Yes, the formula to calculate the surface area of a cone is:
Surface Area = πr(r + l)
where:
- π is pi (approximately 3.14)
- r is the radius of the cone
- l is the slant height of the cone
To find the radius, divide the diameter by 2:
radius = diameter/2 = 12 ft / 2 = 6 ft
Now we can substitute the values into the formula:
Surface Area = 3.14 * 6(6 + 14)
Calculating inside the parentheses: 6 + 14 = 20
Surface Area = 3.14 * 6 * 20
Multiply: 3.14 * 6 * 20 = 376.8
Therefore, the surface area of the cone is approximately 376.8 square feet.
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)
To find the surface area of the cone, we need the slant height (l), not the hypotenuse. However, we can use the given information to find the slant height using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the radius (r) is one side of the right triangle, and the slant height (l) is the hypotenuse. Therefore, we can use the Pythagorean theorem as follows:
r^2 + h^2 = l^2
Substituting the given values:
6^2 + h^2 = 11^2
36 + h^2 = 121
h^2 = 121 - 36
h^2 = 85
h = √85
Now that we have the slant height (l) which is approximately 9.2, we can proceed to calculate the surface area of the cone.
The formula for the surface area of a cone is:
Surface Area = πr(r + l)
Substituting the given values:
Surface Area = 3.14 * 6(6 + 9.2)
Surface Area = 3.14 * 6(15.2)
Surface Area = 3.14 * 91.2
Calculating: 3.14 * 91.2 ≈ 286.368
Therefore, the surface area of the cone is approximately 286.4 square units.
Can you give me another answer as that one incorrect and didn't work?
Apologies for the incorrect answer. Let's recalculate it correctly based on the given values.
Given:
Radius (r) = 6 units
Slant height (l) = 11 units
The formula for the surface area of a cone is still:
Surface Area = πr(r + l)
Substituting the given values:
Surface Area = 3.14 * 6(6 + 11)
Surface Area = 3.14 * 6(17)
Surface Area = 3.14 * 102
Calculating: 3.14 * 102 ≈ 319.68
Rounding to the nearest tenth, the surface area of the cone is approximately 319.7 square units.