Question

Case Study Based IV

Bird-Bath

A bird-bath 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 2

(ii) 2.7 2

(iii) 3.9 2

(iv) 4.3 2

(b) The curved surface area of the hemisphere is approximately:

(i) 0.6 2

(ii) 3.5 2

(iii) 1.52

(iv) None of these

(c) The volume of hemisphere is approximately:

(i) 0.06 3

(ii) 2.8 3

(iii) 5.7 3

(iv) None of these

Refer to Bird-Bath (ii)

(d) The surface area of the conical depression of the bird-bath is approximately:

(i) 0.4 2

(ii) 0.6 2

(iii) 0.7 2

(iv) None of these

(e) The volume of conical depression approximately:

(i) 0.2 3

(ii) 0.3 3

(iii) 4 3

(iv) None of these



This is case study questions
please given me the answer fast ​

Answer 1

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 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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