Mayank a student of class 7th loves watching and playing with birds of different kinds. One day he had an idea in his mind to make a bird-bath on his garden. His brother who is studying in class 10th helped him to choose the material and shape of the birdbath. They made it in the shape of a cylinder with a hemispherical depression at one end as shown in the figure below. They opted for the height of the hollow cylinder as 1.45m and its radius is 30cm.
30 cm
1.45 m
By using the above information, find the following:
a) The curved surface area of the hemisphere is :
(i) 0.36m2 (ii) 0.45m2 (iii) 0.26m2 (iv) 0.56m2
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
The total surface area of the bird-bath
The total surface area of the cylinder
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 :
= 0.56 m²
curved surface area of the cylinder = 2πrh
= 2 π (0.3)(1.45)
= 0.87 π m²
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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Answer:
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