Question

y
The interior of a building is in the form of a cylinder of diameter 4.3m and
height.3.8m, surmounted by a cone whose vertical angle is a right
angle.
4.3
3.8 m :
-4.3 m​

Answer 1

Answer:

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Step-by-step explanation:

Radius of the base of the cylinder r

1

=

2

4.3

m=2.15m

Radius of base of the cone =r

1

=2.15m

Height of the cylinder h

1

=3.8m

In △VOA we have

sin45

o

=

VA

OA

⇒

2

1

=

VA

2.15

⇒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