Math, asked by Vaishnavikeshri4962, 1 year ago

A right angled triangle with sides 12 cm and 16 cm is revolved around its hypotenuse find the volume of the double cone so formed

Answers

Answered by josimagic
12

Answer:

The volume of the double cone so formed  = 1929.21 cm^3

Step-by-step explanation:

From the figure attached with this answer  consists of two cone.

The slant height of each cone is 16 cm and 12 cm respectively.

Let x be the base radius of each cone.

h be the height of large cone and 20 - h be the height of small cone

To find h and (20 -h)

From the figure we get,

x^2 = 16 ^2 - h^2   ------(1)

x^2 = 12^2 - (20 - h)^2     ----(2)

16 ^2 - h^2  = 12^2 - (20 - h)^2

256 = 144 -400 -40h

h = 64/5 = 12.8 cm

there fore height of small cone 20 - h = 20 - 12.8 = 7.2cm

To find x

x^2 = 16^2 - h^2 = 256 - 12.8^2 = 92.16

x =9.6 cm

Volume of cone

V = 1/3[πr^2h]

To find the volume of large cone

V1 = 1/3[πr^2h] = 1/3[3.14 x 9.6 x 9.6 x 12.8] = 1234.7 cm^3

To find the volume of large cone

V2 = 1/3[πr^2h] = 1/3[3.14 x 9.6 x 9.6 x 7.2] = 694.5 cm^3

Total volume

Volume V = v1 +v2 = 1234.7 + 694.5 =1929.21 cm^3


Attachments:
Answered by smjothibasu
3

Answer:

rom the figure attached with this answer  consists of two cone.

The slant height of each cone is 16 cm and 12 cm respectively.

Let x be the base radius of each cone.

h be the height of large cone and 20 - h be the height of small cone

To find h and (20 -h)

From the figure we get,

x^2 = 16 ^2 - h^2   ------(1)

x^2 = 12^2 - (20 - h)^2     ----(2)

16 ^2 - h^2  = 12^2 - (20 - h)^2

256 = 144 -400 -40h

h = 64/5 = 12.8 cm

there fore height of small cone 20 - h = 20 - 12.8 = 7.2cm

To find x

x^2 = 16^2 - h^2 = 256 - 12.8^2 = 92.16

x =9.6 cm

Volume of cone

V = 1/3[πr^2h]

To find the volume of large cone

V1 = 1/3[πr^2h] = 1/3[3.14 x 9.6 x 9.6 x 12.8] = 1234.7 cm^3

To find the volume of large cone

V2 = 1/3[πr^2h] = 1/3[3.14 x 9.6 x 9.6 x 7.2] = 694.5 cm^3

Total volume

Volume V = v1 +v2 = 1234.7 + 694.5 =1929.21 cm^3

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