Question

Rahul an Engineering student, prepared a model shaped like a cylinder with two cones attached to its ends. the diameter of model is 3cm and it's length is 12cm .If each conical part has the height of 2 cm, Find the (i) volume of air contained in Rahul's model (ii) cost of painting of the outer surface area of the model at 12.50 per cm³​

Answer 1

Answer:

For the given statement first draw a diagram,

In this diagram, we can observe that

Height (h

1

) of each conical part =2 cm

Height (h

2

) of cylindrical part 12−2−2=8 cm

Radius (r) of cylindrical part = Radius of conical part =

2

3

cm

Volume of air present in the model = Volume of cylinder + 2× Volume of a cone

=πr

2

h

2

+2×πr

2

h

1

=π(

2

3

)

2

×8+2×

3

1

π(

2

3

)

2

(2)

=π×

4

9

×8+

3

2

π×

4

9

×2

=18π+3π=21π

=21×

7

22

=66 cm

2

Answer 2

Answer:

Height of each conical part, h = 2 cm.

Length of the cylindrical part, h = (12 - 2 2)cm = 8 cm.

Slant height of each conical part,

l =

$\sqrt{ {r}^{2} + {h}^{2} }$

$\sqrt{ {3 \div 2}^{2} + {2}^{2} }$

$\sqrt{9 \div 4 + 2}$

$\sqrt{25 \div 4}$

$5 \div 2 \: cm$

or 2.5 cm

(i) Volume of air contained in the mode = volume of 2 conical parts + volume of the cylindrical part

=

2 * 1/3 πr*r*h + πr*r*h

πr*r (2/3 h + H)

22/7 * 3/2 *3/2 (2/3 *2 +8)

22/7 * 3/2 * 3/2 * 28/3

= 66 cm^3

(ii) Total surface area of the model = curved surface area of 2 conical parts + curved surface area of the cylindrical part

= 2πrl + 2πrH

= 2πr(l+ h)

= 2 * 22/7 * 3/2 (5/2 +8)

= 2* 22/7 * 3/2 ( 5 + 16 / 2)

= 99 cm^2

cost of painting the model = Rs. (99 * 12.50)

= Rs. 1237.50.