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A godown building as shown in figure is made in the form of a cubical base with dimensions $40 m \times 14 m \times 4 m$ , surmounted by a half cylindrical curved roof having same length as that of the base. The diameter of the cylinder is $14 m$ . Find the volume of the building and its total outer surface area.

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Volume =

5310 m^{3};

Outer Surface Area =

1466 m^{2}

Volume =

5310 m^{3};

Outer Surface Area =

1486 m^{2}

Volume =

5320 m^{3};

Outer Surface Area =

1466 m^{2}

Volume =

5320 m^{3};

Outer Surface Area =

1486 m^{2}

answer is C.

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Detailed Solution

It is given,
Question Image

Volume of building

=

volume of cuboid + volume of half cylinder

\Rightarrow l \times b \times h + \frac{1}{2} π r^{2} h

\Rightarrow (40 \times 14 \times 4) + \frac{1}{2} \times \frac{22}{7} \times \frac{14}{2} \times \frac{14}{2} \times 40

\Rightarrow 2240 + 3080

\Rightarrow 5320 m^{3}

Total outer surface area

= 2 h (l + b) + \frac{1}{2} π r^{2} h + π r^{2}

\Rightarrow 2 \times 4 (40 + 14) + \frac{22}{7} \times 7 \times 40 + \frac{22}{7} \times 7 \times 7

\Rightarrow 8 \times 54 + 22 \times 40 + 22 \times 7

\Rightarrow 1466 m^{2}

Therefore, the volume of the building and its total outer surface area is

5320 m^{3}

and

1466 m^{2}

.
Hence, the correct option is 3.

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A godown building as shown in figure is made in the form of a cubical base with dimensions 40m×14m×4m, surmounted by a half cylindrical curved roof having same length as that of the base. The diameter of the cylinder is 14m. Find the volume of the building and its total outer surface area.

Detailed Solution

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