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A godown building is in the form as shown in the figure.

The vertical cross section parallel to the width side of the building is a rectangle of dimensions $7 m × 3 m$ , mounted by semicircle of radius $3.5 m$ . The inner measurements of the cuboidal portion of the building are $10 m × 7 m × 3 m$ . Find the volume of godown.

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400.455 m 3

402.325 m 3

302.365 m 3

202.325 m 3

answer is B.

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Detailed Solution

Given a godown building,
Question Image

The volume of the cuboid is,

V = l × b × h

, where l is length, b is breadth, h is height.
Volume of cuboid part =

10 m × 7 m × 3 m

⇒ 210 m 3

Volume of semicylinder =

12 π r 2 l

where, r is radius, l is length of cylinder.
Volume of semicylindrical part =

12 π (3.5) 2 10

⇒ 3.14 × 12.25 × 5 ⇒ 192.325 m 3

Now, total volume of godown = volume of cuboid + volume of semicylinder
Total volume =

210 m 3 + 192.325 m 3

⇒ 402.325 m 3

Thus, the volume of the godown is

402.325 m 3

.
Therefore, option (2) is correct.

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