Question

CASE STUDY: STUDY OF FIGURES AND SHAPES

Sam 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. They opted for the height of the hollow

cylinder as 1.45 m and its radius is 30 cm.

By using the above-given information, find the following:

i) The curved surface area of the hemisphere is:

a) 0.36 m2

b) 0.46 m2

c) 0.26 m2

d) 0.56 m2

ii) The curved surface area of the cylinder is:

a) 0.78Π m2

b) 0.87

2

Π m2

c) 0.87Π2 m2

d) 0.87Π m2

iii) The total surface area of the bird-bath is: (Take Π = 22

7

)

a) 2.3 m2

b) 3.3 m2

c) 3.5 m2

d) 5.3 m2

iv) The total surface area of the cylinder is given by:

a) 2Πrh + 2Πr3 b) 2Πrh + Πr2

c) 2Πrh + 2Πr2 d) Πrh + 2Πr2

v) During the conversion of a solid from one shape to another the volume of the new shape will :

a) Remain unaltered b) Decrease

c) Double d) Increase​

Answer 1

QUESTION 1 ANSWER = 0.36M2

QUESTION 2 ANSWER = 0.87

QUESTION 3 ANSWER = 3.3M2

QUESTION 4 ANSWER = double

Answer 2

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 is:

The curved surface area of the cylinder is:

The total surface area of the bird-bath

The total surface area of the cylinder is given by:

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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