Question

A godown building as shown in figure is made in the form of a cubical base with dimensions $40m\times 14m\times 4m$, 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.

• A. Volume = $5310m^3;$ Outer Surface Area = $1466m^2$
• B. Volume = $5310m^3;$ Outer Surface Area = $1486m^2$
• C. Volume = $5320m^3;$ Outer Surface Area = $1466m^2$
• D. Volume = $5320m^3;$ Outer Surface Area = $1486m^2$

Answer 1

Answer: (C)

Volume = $5320m^3;$ Outer Surface Area = $1466m^2$

Volume of the building $=$ Volume of cuboid $+$ Volume of cylindrical top

$=40\times 14\times 4+\frac{1}{2}\times \pi \times 7^2\times 40=2240+3080=5320m^3$

Total surface area $=$ Surface area of cuboid $+$ Surface area of cylindrical surface $+$ Area of a circle

$=2(40\times 4+14\times 4)+\pi \times 7\times 40+\pi {\times 7}^2=432+880+154=1466m^2$