Find the curved and total surface area of a right circular cone,of base radius 8cm and height 10cm
at a farmers market you buy 4 lbs of tomatoes and 2 lbs. of sweet potatoes.
plug your numbers into the formulas found here:
https://www.google.com/search?q=cone+area&ie=utf-8&oe=utf-8
1.B
2.A
3.C
4.D
5.A
6.A
7.A
To find the curved surface area of a cone, we need to calculate the area of the curved surface that forms the lateral side of the cone. Similarly, the total surface area of the cone is the sum of the curved surface area and the area of the base.
Let's calculate the curved surface area (CSA) first:
The formula to find the CSA of a cone is given by:
CSA = π * r * l
where r is the base radius of the cone and l is the slant height.
To find l, we can use the Pythagorean theorem. The slant height forms a right triangle with the height (h) and the radius (r) of the cone. The slant height is the hypotenuse of this triangle.
Using the Pythagorean theorem:
l² = r² + h²
Plugging in the values, we get:
l = √(r² + h²)
Given:
Base radius (r) = 8 cm
Height (h) = 10 cm
Substituting the values, we have:
l = √(8² + 10²)
l = √(64 + 100)
l = √164
l ≈ 12.81 cm (rounded to two decimal places)
Now, we can calculate the CSA:
CSA = π * r * l
CSA = π * 8 * 12.81
CSA ≈ 322.08 cm² (rounded to two decimal places)
To find the total surface area (TSA), we also need to calculate the area of the base.
The formula to find the area of a circle is:
A = π * r²
Given:
Base radius (r) = 8 cm
Substituting the value, we have:
A = π * 8²
A = π * 64
A ≈ 201.06 cm² (rounded to two decimal places)
To find the TSA, we sum the CSA and the area of the base:
TSA = CSA + A
TSA ≈ 322.08 + 201.06
TSA ≈ 523.14 cm² (rounded to two decimal places)
Therefore, the curved surface area of the cone is approximately 322.08 cm², and the total surface area is approximately 523.14 cm².