Multiple choice

A solid cone of radius $r$ and height $h$ is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is

  1. $\pi r\left [ \sqrt{r^{2}+h^{2}}+3r+2h \right ]$
  2. $\pi r\left [ \sqrt{r^{2}+h^{2}}+2r+3h \right ]$
  3. $\pi r\left [2 \sqrt{r^{2}+h^{2}}+3r+2h \right ]$

  4. none of these
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A Correct answer
AI explanation

The total surface area of the combined solid is found by adding the curved surface area of the cylinder to the curved surface area of the cone and the base area of the combined shape. The curved surface area of the cylinder is 2 times pi times r times h, the curved surface area of the cone is pi times r times the square root of (r squared plus h squared), and the single circular base at the bottom is pi times r squared. Adding these three components together and factoring out pi times r yields the expression pi times r times the square root of (r squared plus h squared) plus 2h plus 3r. The result is pi times r times the square root of (r squared plus h squared) plus 3r plus 2h.

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