Cal d total surface area of a solid cone of slant height 15cm and base radius 8cm in term of pie
π*8(8+15)
And that's pi, not pie!
Pie is what you eat.
To calculate the total surface area of a solid cone, we need to consider two components: the curved surface area (CSA) and the base area.
1. Curved Surface Area (CSA):
The CSA can be thought of as the lateral surface of the cone. It is calculated by finding the area of the sector formed by unrolling the curved surface and laying it flat. The radius of this sector is the slant height of the cone, and the arc length is the circumference of the cone's base.
To find the CSA, we use the formula: CSA = π × r × l
where r is the radius of the base and l is the slant height.
In this case, the radius of the base (r) is given as 8 cm, and the slant height (l) is given as 15 cm. Plugging these values into the formula, we get:
CSA = π × 8 × 15
2. Base Area:
The base area of a cone is given by the formula A = π × r^2, where r is the radius of the base.
In this case, the radius of the base is 8 cm, so the base area is:
Base Area = π × 8^2
To find the total surface area of the cone, we add the CSA and the base area together:
Total Surface Area = CSA + Base Area
Putting it all together, the total surface area of the solid cone is:
Total Surface Area = π × 8 × 15 + π × 8^2
Simplifying further, you can factor out π:
Total Surface Area = π × (8 × 15 + 8^2)
Thus, the total surface area of the solid cone in terms of π is:
Total Surface Area = π × (120 + 64)
Total Surface Area = π × 184 cm^2