Calculate the total surface area of a solid cone of:
Base radius 6cm and slant height 10cm
A = πr(r+s)
so plug in your numbers
To calculate the total surface area of a solid cone, we need to find the sum of the areas of the base and the lateral surface.
1. Base Area:
The base of the cone is a circle, and the formula to find the area of a circle is A = πr^2, where A represents the area and r represents the radius.
Given the base radius is 6 cm, we can substitute that into the formula:
Base Area = π * (6 cm)^2
Base Area = π * 36 cm^2 (approx. 113.04 cm^2)
2. Lateral Surface Area:
The lateral surface of the cone is a curved surface, and the formula to find its area is A = πrl, where A represents the area, r represents the radius, and l represents the slant height.
Given the radius is 6 cm and the slant height is 10 cm, we can substitute those values into the formula:
Lateral Surface Area = π * 6 cm * 10 cm
Lateral Surface Area = π * 60 cm^2 (approx. 188.5 cm^2)
3. Total Surface Area:
To calculate the total surface area, we need to add the base area and the lateral surface area together.
Total Surface Area = Base Area + Lateral Surface Area
Total Surface Area = π * 36 cm^2 + π * 60 cm^2
Total Surface Area = π * 96 cm^2 (approx. 301.54 cm^2)
Therefore, the total surface area of the solid cone is approximately 301.54 cm^2.