To calculate the total surface area of a solid cone, we need to find the area of the curved surface (lateral surface) as well as the base.
The curved surface area (CSA) of a cone can be calculated using the formula:
CSA = π × r × l
where r is the radius of the base of the cone and l is the slant height.
We are given the slant height (l) to be 25 cm, and the vertical height (h) to be 24 cm. To find the radius (r) of the base, we can use the Pythagorean theorem:
r = √(l^2 - h^2)
= √(25^2 - 24^2)
= √(625 - 576)
= √49
= 7 cm
Now, we can calculate the curved surface area:
CSA = π × r × l
= π × 7 × 25
= 175π cm²
To find the base area, we can use the formula for the area of a circle:
Base area = π × r^2
= π × 7^2
= 49π cm²
The total surface area (TSA) of the solid cone is the sum of the curved surface area and the base area:
TSA = CSA + Base area
= 175π + 49π
= 224π cm²
Therefore, the total surface area of the solid cone is 224π square centimeters.
Calculate the total surface area of a solid cone of slant height of 25cm and vertical height of 24cm
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