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The interior of a building is in the form of cylinder of diameter $4.3 m$ and $4.3 m$ height, surmounted by a cone whose vertical angle is a right angle. What is the volume of building?

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65 m 3

65.55 m 3

64.44 m 3

64 m 3

answer is B.

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Detailed Solution

Given that cylinder of diameter

4.3 m

and its height is

3.8 m

.
We have the following formulae,
Volume of cylinder

= π (r) 2 h

Volume of cone

= 13 π (r) 3

sin θ = h e i g h t h y p o t e n u s e

In △VOA,

sin 45 o

O A V A

12 = 2.15 V A

V A = 2 × 2.15 m = 3.04 m

We see that

Δ V O A

is an isosceles triangle, then,

V O = O A = 2.15 m

We take

r 1, h 1

as the radius and the height of the cylinder.
The height and radius of the cylinder will be,

h 1 = 3.8 r 1 = 2.15

Height of the cone will be,

h 2 = V O h 2 = 2.15 m

Slant height of the cone will be,

l 2 = V A l 2 = 3.04 m

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

= π r 12 h 1 + 13 π r 12 h 2 m 3 = π r 12 h 1 + 13 h 2 m 3

= 3.14 × 2.15 × 2.15 × 3.8 + 2.15 3 m 3

= 65.55 m 3

Thus the volume of the building is

65.55 m 3

.
Therefore the correct option is 2.

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