Math, asked by nidhipoppins1525, 11 months ago

Interior of a building is in the form of a cylinder of diameter 4.3 metre and height 3.8 mounted by a cone whose vertical angle is right angle find the area of the surface and volume of the building

Answers

Answered by knjroopa
26

Step-by-step explanation:

Given Interior of a building is in the form of a cylinder of diameter 4.3 metre and height 3.8 mounted by a cone whose vertical angle is right angle find the area of the surface and volume of the building

Radius of cone is equal to radius of cylinder.

                = 4.3 / 2

              = 2.15 m

Now in triangle ABC = 45 degree

So tan 45 = BC / AB

     1 = 2.15 / AB

     AB = 2.15

So height of the cone is 2.15 m.

Volume of building = volume of cylinder + volume of cone.

                               = π (2.15)^2 x 3.8 + 1/3 π (2.15)^2 x 2.15

                               = π (17.5655 + 3.3127)

                                = 3.14 x 20.8782

                               = 65.56 m^3

    Now slant height of the cone is l = √2.15^2 + 2.15^2

                                                         = 3.04 m

Now surface area of the building = surface area of cylinder + surface area of cone

                                                  = 2 π x 2.15 x 3.8 + π x 2.15 x 3.04

                                                  = π (16.34 + 6.536)

                                                   = 3.14 x 22.876

                                                   = 71.83 sq m

Reference link will be

https://brainly.in/question/2365792

Answered by st252649
0

Answer

r 1=4.3/2

m=2.15m

Radius of base of the cone =r2

=2.15m

Height of the cylinder h1

=3.8m

In △VOA we have

sin45 o = VA/OA

21 = VA2.15

⇒VA=(

2

×2.15)m=3.04m

Clearly △VOA is an isosceles triangle

Therefore, VO=OA=2.15m

Thus, we have

height of the cone =h

2

=VO=2.15m

Slant height of the ocne l

2

=VA=3.04m

Surface area of the building = Surface area of the cylinder + Surface area of cone

=(2πr

1

h

1

+πr

2

l

2

)m

2

=(2πr

1

h

1

+πr

1

l

2

)m

2

=πr

1

(2h

1

+l

2

)m

2

=3.14×2.15×(2×3.8+3.04)m

2

=3.14×2.15×10.64m

2

=71.83m

2

Volume of the building = volume of the cylinder + volume of the cone

=(πr

1

2

h

1

+

3

1

πr

2

2

h

2

)m

3

=(πr

1

2

h

1

+

3

1

πr

1

2

h

2

)m

3

[∵r

2

=r

1

]

=πr

1

2

(h

1

+

3

1

h

2

)m

3

=3.14×2.15×2.15×(3.8+

3

2.15

)m

3

=65.55m

3

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