Question

Kartike, an engineering student was asked to make a model in his workshop, which was shaped like cylinder with two equal cones attached at its two ends;the diameter of the model is 3.5 cm and its length is 18 cm, if each cone has a height of 4 cm. Find the volume of the model that Kartike made.​

Answer 1

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>>Surface Areas and Volumes

>>Volume of Combined Solids

>>kartik, an engineering student, kartikwas ask

an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

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Hard

Solution

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Correct option is A)

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:

Vol. of model = 2 × vol. of cone + vol. of cylinder

$\sf \: vol. \: of \: cone \: = \frac{1}{3} \pi {r}^{2} h = \frac{1}{3} \times \frac{22}{7} \times 1.75 {}^{2} \times 4$

$\sf \: = 12.833 \: c {m}^{3}$

Volume of two cone = 2× 12.833 = 25.66

$\sf \: vol. \: of \: cylinder \: = \pi {r}^{2} h$

h = 18 - 8 = 10 cm

$\sf \: vol. \: of \: cone \: = \pi {r}^{2} h = \frac{22}{7} \times 1.75 {}^{2} \times 10 \\ \\ \sf \: = 96.25 \: {cm}^{3}$

Total volume = 25.66+ 96.25 121.91 cubic cm