Question

Write ‘True’ or ‘False’ and justify your answer

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 $\pi r\sqrt{r^2+h^2}+3r+2h$

Answer 1

The given statement is false.

We know that,
The total surface area of a cone of radius r
and height h
= curved surface Area + area of base
$=\pi rl+\pi r^2$

Where, $l=\sqrt{h^2+r^2}$

The total surface area of a cylinder of base radius r and hegith h
= Curved surface area + Area of both base
$=2\pi rh+2\pi r^2$

Here, when we placed a cone over a cylinder, then one base is common for both.

So, total surface area of the combined solid
$=\pi rl+2\pi rh+\pi r^2$
$=\pi [l+2h+r]=\pi r[\sqrt{r^2+h^2}+2h+r](\because l=\sqrt{r^2+h^2})$