Find the total surface area of a right circular cone, if the height and radius of the cone are 63 cm and 16 cm, respectively.
1296π cm2
The total surface area of a cone is given by:
Surface area = πr(r + l),
where r is the radius and l is the slant height of the cone.
We are given the radius r = 16 cm and the height h = 63 cm. First, we calculate the slant height l using the Pythagorean theorem:
l = √(r2 + h2) = √(162 + 632) = √(256 + 3969) = √4225 = 65 cm
Now, substitute the values into the surface area formula:
Surface area = π × 16 × (16 + 65) = π × 16 × 81 = 1296π cm2
The total surface area of the cone is 1296π cm2.
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