Question & Answer
QUESTION

The total surface area of the given solid figure is –

ANSWER Verified Verified
Hint – Use the formula, total surface area = curved surface area of cone + curved surface area of cylinder + area of base. And then solve.

Complete step by step answer:
According to the question, we have to find the total surface area of the given figure.
So, we can say the total surface area of the figure = curved surface area of cone + curved surface area of cylinder + area of base.
Now, the curved surface area of cylinder $CS{A_1} = 2\pi rh$.
Curved surface area of cone, $CS{A_2} = \pi rl$.
And, area of base, $B = \pi {r^2}$.
Here, r = radius, h = height, l = slant height.
So, now the total surface area of the given figure will be, $A = CS{A_1} + CS{A_2} + B$,
Keeping the values of $CS{A_1} = 2\pi rh$, $CS{A_2} = \pi rl$, $B = \pi {r^2}$in A, we get-
$
  A = 2\pi rh + \pi rl + \pi {r^2} \\
   = \pi r(2h + l + r)sq.units \\
$
Hence, the total surface area of the given figure is, $ = \pi r(2h + l + r)sq.units$.

Note – While solving such types of questions, see the figure is made of what combinations, as here in the given question, the figure contains a cone and a cylinder. Hence, the total surface area will be the sum of the curved surface area of both the figure and the area of the base.