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
=πrl+πr2
Where, l=√h2+r2
The total surface area of a cylinder of base radius r and hegith h
= Curved surface area + Area of both base
=2πrh+2πr2
Here, when we placed a cone over a cylinder, then one base is common for both.
So, total surface area of the combined solid
=πrl+2πrh+πr2
=π[l+2h+r]=πr[√r2+h2+2h+r] (∵l=√r2+h2)