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

Open in App

Solution

Let $r_{1}$ be the radius of base of the cylinder and $h_{1}$ m be its height. Then,

$r_{1} = 2.1 m; h_{1} = 4 m$

Let $r_{2}$ m be the radius of the base of the cone, $h_{2}$ m be its height and $l_{2}$ m and be its slant height. Then,

$r_{2} = 2.1 m; h_{2} = 2.1 m$

$∴ l_{2}^{2} = r_{2}^{2} + h_{2}^{2} \Rightarrow l_{2} = \sqrt{r_{2}^{2} + h_{2}^{2}} \Rightarrow l_{2} = \sqrt{{(2.1)}^{2} + {(2.1)}^{2}} = 2.1 \times \sqrt{2} m$

Now Outer surface area of the building = curved surface are of cylinder + Curved surface area of cone

$= (2 π r_{1} h_{1} + π r_{2} l_{2}) m^{2} = π (2 r_{1} h_{1} + r_{2} l_{2}) m^{2}$

$= \frac{22}{7} (2 \times 2.1 \times 4 + 2.1 \times 2.1 \times \sqrt{2}) m^{2} = \frac{22}{7} \times 2.1 \times 10.9694 m^{2} = 72.3980 m^{2} = 72.40 m^{2}$

volume of the building = volume of the cylinder + volume of the cone

$= (π r_{1}^{2} h_{1} + \frac{1}{3} π r_{2}^{2} h_{2}) m^{3} = (π r_{1}^{2} h_{1} + \frac{1}{3} π r_{1}^{2} h_{2}) m^{3} [∵ r_{2} = r_{1}]$

$= π r_{1}^{2} (h_{1} + \frac{1}{3} h_{2}) m^{3}$

$= \frac{22}{7} 2.1 \times 2.1 \times (4 + \frac{1}{3} \times 2.1) m^{3} = 65.142 m^{3}$

Suggest Corrections

Similar questions

The interior of a building is in the form of a right circular cylinder of diameter 4.2 m and height 4 m surmounted by a cone of same diameter. The height of the cone is 2.8 m. Find the outer surface area of the building.

Q. The interior of a building is in the form of cylinder of diameter

4.3 m

and height

3.8 m

surrounded by a cone whose vertical angle is a right angle. Find the area of the surface and the volume of the building (Take

π = 3.14

)

Q. The interior of a building is in the form of a cylinder of base radius 12 m and height 3.5 m, surmounted by a cone of equal base and slant height 12.5 m. Find the internal curved surface area and the capacity of the building.

Q. A tent of height

77 d m

is in the form of a right circular cylinder of diameter

36 m

and height

44 d m

surmounted by a right circular cone. Find the cost of the canvas at Rs.

3.50

per

m^{2}

(Use

π = 22 / 7

)

Q. A tent of height 77 dm is in the form a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs 3.50 per m². [Use π = 22/7]

Join BYJU'S Learning Program

The interior of a building is in the form of a right circular cylinder of diameter 4.2m and height 4m surrounded by a cone. The vertical height of cone is 2.1m. Find the outer surface area and volume of the building. (Use π=22/7)

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