Multiple choice

A right circular cone has height 8 cm. If the radius of its base is 6 cm, then what is its total surface area?

  1. 96π cm2

  2. 69π cm2

  3. 54π cm2

  4. 48π cm2
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A Correct answer
Explanation

The slant height l is sqrt(r^2 + h^2) = sqrt(6^2 + 8^2) = 10 cm. The total surface area is pi*r*(r + l) = pi*6*(6 + 10) = 96pi cm^2.

AI explanation

Using the Pythagorean theorem, the slant height is the square root of the sum of the squares of the height and radius, which is the square root of 64 plus 36, giving 10 cm. The total surface area of a cone is found by adding the curved surface area and the base area: pi multiplied by the radius multiplied by the slant height plus pi multiplied by the square of the radius. This calculates to 60 times pi plus 36 times pi, totaling 96 times pi square cm.

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