Multiple choice

The height of a solid cylinder is 8 cm and its base radius is 6 cm, a cone of equal height and the radius is extracted from the cylinder, then find the total surface area of the remaining solid.

  1. 6π cm2

  2. 36π cm2

  3. 192π cm2

  4. 16π cm2

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original cylinder: r = 6 cm, h = 8 cm. After removing cone with same dimensions, the remaining solid has: exposed top ring (outer circle minus cone base) = π(6² - 6²) = 0, curved surface of remaining cylinder portion = 2π(6)(8) = 96π, and base of cylinder = π(6²) = 36π. Also includes inner curved surface (cone lateral area removed) = π(6)(√(6² + 8²)) = 60π. Total = 96π + 36π + 60π = 192π sq.cm. Note: the cone removal creates a cylindrical cavity with curved surface.