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.

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 πr[√(r² + h² +3r + 2h].

Answer 1

False

Explanation:

When a solid cone is placed over a solid cylinder of same base radius, the base of cone and top of the cylinder will not be covered in total surface area.

Since the height of cone and cylinder is same,

We get,

Total surface area of cone = πrl + πr², where r = base radius and l = slant height

Total surface area of shape formed = Total surface area of cone + Total Surface area of cylinder – 2(Area of base)

Total surface area of cylinder = 2πrh + 2πr²h, where r = base radius and h = height

= πr(r + l) + (2πrh + 2πr²) – 2(πr²)

= πr² + πrl + 2πrh + 2πr² – 2πr²

= πr(r + l + h)