Question

find the volume and surface area of circular or cylindrical body surrounded by a cone

Answer 1

In the attachment I have drawn the given adjoining figure.

Volume and surface area of adjoining figure has been calculated in a easy way.

I hope this answer helps you

Answer 2

Refers to the attachment for the Diagram.

We know,
 Volume of the Cylinder = πr²H
Volume of the Cone = 1/3 × πr²h

Here,
H = Height of the Cylinder.
h = height of the cone
r = radius of the cone and radius of the Cylinder 
[∵ The base of both of them coincides]

∴ Volume of the Figure = Volume of the cone + Volume of the Cylinder
∴ Volume of the Figure = 1/3 × πr²h + πr²H
 = πr² [h/3 + H]
 = πr²[( h + 3H)/3]
 = 1/3 × π r²(h + 3H)

_____________________________

Now, For the Surface area,
Curved surface area of the cone = πrl
where,  l is the slant height of the cone.

Curved Surface area of the Cylinder = 2πrH
Area of the base of the cylinder = πr²

∴ Surface area of the Figure = πrl + 2πrH + πr²
  =  πr(l + 2H + r)

Hence, the Surface area of the Figure is  πr(l + 2H + r)


Hope it helps.