The interior of a building is in the form of a cylinder of diameter 4.3 m and height 3.8 m surmounted 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]

The diameter of a cylindrical portion BCDE of building = 4.3m

∴ The radius of a cylindrical portion

Height = 3.8m

Lateral Surface Area of Cylindrical Portion BCDE = 2πrh

= 51.3543 m²

Let AB be the slant height of the conical portion of the building = l = AB = AC

Now, the Lateral surface of conical portion = πrl

= 20.5417 m²

So,

The total surface area of the building = Surface area of cylindrical portion + Surface area of the conical portion

= 51.3543 + 20.5417

= 71.8960

= 71.90 m² (approx.)

Now, In right ΔBAC,

BC² = AB² + AC²

⇒ BC² = l² + l²

⇒ (4.3)² = 2l²

⇒ 18.49 = 2l²

⇒ l² = 9.245

⇒ l = 3.04 m

Here, r is the radius of the cone and l is the slant height of the cone

⇒ l² = h² + r²

⇒ 9.245 = h² + (2.15)²

⇒ 9.245 = h² + 4.6225

⇒ h² = 9.245 – 4.6225

⇒ h² = 4.6225

⇒ h = 2.15 m

Now, Volume of the conical portion

= 10.4116 m³

Volume of cylindrical portion BCDE = πr²h

= 55.2059 m³

So,

The total volume of the building = Volume of the cylindrical portion

+ Volume of the conical portion

= 55.2059 + 10.4116

= 65.6175 m³

= 65.62 m³ (approx.)