Question

The interior of a building is in the form of a right circular cylinder of a diameter 4.2 m and height 4 m, surmounted by a cone. The vertical height of the cone is 2.1 m. Find the outer surface area and volume of the building.(Take $\pi$ = 22/7)

• A. Outer surface area$=72.4m^2;$ Volume$=68.142m^3$
• B. Outer surface area$=72.4m^2;$ Volume$=65.142m^3$
• C. Outer surface area$=75.4m^2;$ Volume$=68.142m^3$
• D. Outer surface area$=75.4m^2;$ Volume$=65.142m^3$

Answer 1

The correct option is B Outer surface area$=72.4m^2;$ Volume$=65.142m^3$

Outer Surface area of the building $=$ Curved surface area of cylindrical part $+$ Curved surface area if the conical part. Curved Surface Area of a Cylinder of Radius "R" and height "h" $=2\pi Rh$
Radius of the cylindrical part $=\frac{Diameter}{2}=\frac{4.2}{2}=2.1m$ Curved surface area of a cone $=\pi rl$ where r is the radius of the cone and l is the slant height.

Radius of the conical part $=\frac{Diameter}{2}=\frac{4.2}{2}=2.1m$

For a cone, l $=\sqrt{h^2+r^2}$ where h is the height.

Hence, l $=\sqrt{{2.1}^2+{2.1}^2}$

$l=2.1\sqrt{2}m$
Hence, surface area of building $=(2\times \frac{22}{7}\times 2.1\times 4)+(\frac{22}{7}\times 2.1\times 2.1\sqrt{2})=72.4m^2$
Volume of the building $=$ Volume of the cylindrical part $+$ Volume of conical part
Volume of a Cylinder of Radius "R" and height "h" $=\pi R^{2}h$
Volume of a cone $=\frac{1}{3}\pi r^{2}h$ where r
is the radius of the base of the cone and h is the height.
Hence, Volume of the pillar $=(\frac{22}{7}\times 2.1\times 2.1\times 4)+(\frac{1}{3}\times \frac{22}{7}\times {2.1}^2\times 2.1)=65.142m^3$