The total surface area of the given solid figure is

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s = π r (l + 2 h)

s = π r (l + r)

s = π r (l + 2 h + r)

s = π (l + 2 h + r)

answer is C.

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Detailed Solution

Solid figures: The objects having a definite shape, size and occupies a fixed amount of space in three dimensions are called solids such as a cube, cuboid, cylinder, cone, sphere, and hemisphere, etc. Surface area: The surface area of a solid object is a measure of the total area that the surface of the object occupies and it is always measured in a square unit. Hence the surface area is also known as total surface area TSA.
Given a solid material made up of cylinder mounted by a cone.
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We know that,
Curved surface area of cone

= 2 π r h … … (1)

Also, curved surface area of a cylinder

= 2 π r h … … (2)

Area of cylindrical base

= π r 2 … … (3)

Let us add equations (1), (2) and (3) to get the total surface area of the given figure.
Let the total surface area of the given figure be S.
S = Curved surface area of cone + Curved surface area of cylinder + Area of the cylindrical base.
The total surface area of the given figure,