Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the birth - bath.

$open parentheses bold pi bold space bold equals bold space bold 22 over bold 7 close parentheses bold space bold space$

Solution

Let r cm be the radius and h cm be the height of the cylinder then,
r = 30 cm,
h = 1.45 m = 145 cm.
Lei r₁ cm be the radius of the hemisphere, then
r₁ = 30 cm
Now,
The Total Surface Area of the bird bath
= C.S.A of cylinder + C.S.A of Hemisphere
= 2 $straight pi$ rh + 2 $straight pi$ r₁ ²= 2 $straight pi$ rh + 2 $straight pi$ r² [∵ r = r₁]
= [2 ∵ r (h + r)] cm²

$equals space open square brackets open parentheses 2 straight x 22 over 7 straight x 30 close parentheses left parenthesis 145 space plus space 30 right parenthesis close square brackets space cm squared equals space open parentheses 1320 over 7 straight x 175 close parentheses space cm squared$
= 33000 cm²
= 3.3 m²

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