A bird-sath is a small-container" which is placed in a garden and filled with water for birds to
bath in.
Mayank and Swati both made two bird-baths as their school projects. The shape of Mayank's
bird-bath is a cylinder with a hemispherical depression at one end as shown in figure (A).
whereas the shape of Swati's bird-bath is a cylinder with conical depression at one end as shown
in figure (B)
Bird-Bath (i): The height of hollow cylinder used in making this bird-bath is 1.45m and radius is
30cm.
Bird-Bath (ii): The height of the entire bird-bath is 2.6m, while the height of the conical
depression is 36cm. The radius of the bird-bath is 28cm.
Refer to Bird-Bath (i)
(a) The curved surface area of the cylinder is approximately:
(i) 1.45 m2
(ii) 2.7 m2
(iii) 3.9 m?
(iv) 4.3 m2
(b) The curved surface area of the hemisphere is approximately:
(i) 0.6 m2
(ü) 3.5 m2
(ui) 1.5m?
(iv) None of these
(c) The volume of hemisphere is approximately:
(1) 0.06 m
(i) 2.8 m3
(iii) 5.7 m3
(iv) None of these
Refer to Bird-Bath (ii)
(d) The surface area of the conical depression of the bird-bath is approximately:
fil 0.4 m2
(1) 0.6 m2
(iii) 0.7 m2
(iv) None of these
Answers
Given : birdbath in the shape of a cylinder with a hemispherical depression at one end as shown in the Figure.
height of the hollow cylinder as 1.45 m and its radius is 30 cm.
To Find : The curved surface area of the hemisphere
The curved surface area of the cylinder
volume of hemisphere
Solution:
curved surface area of the hemisphere is: 2πr²
r = 30 cm = 0.3 m
=> curved surface area of the hemisphere = 2(22/7)(0.3)²
= 0.5657
from given options :
= 0.6 m²
curved surface area of the cylinder = 2πrh
= 2 π (0.3)(1.45)
= 0.87 π
= 2.73 m²
= 2.7 m²
volume of hemisphere = (2/3)πr³ = 0.056 = 0.06 m³
The total surface area of the bird-bath = base + curved cylinder + curved hemisphere =
πr² + 2πrh + 2πr²
= 2πrh + 3πr²
= 3.57 m²
if base not includes then
2πrh + 2πr² = 3.3 m²
The total surface area of the cylinder is given by: 2πrh + πr2 ( as open from top)
During the conversion of a solid from one shape to another the volume of the new shape will : Remain unaltered
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