Question

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]

Answer 1

Diameter= 4.3 m

Radius = 2.15 m

Height = 3.8 m

Lateral Surface Area of cylindrical portion = 2πrh

⇒ 2*22/7*2.15*3.8

= 359.48/7

= 51.3543 cm^2

⇒ l² + l² = (BC)² (BC = diameter of the common base of cone and cylinder)

⇒ 2l² = (4.3)²

⇒ 2l² = 18.49

⇒ l² = 18.49/2

⇒ l = 3.04 m

l² = r² + h²

(3.04)² = √(2.15)² + h²

9.2416 = 4.6225 + h²

h = √4.6191

h = 2.149 or 2.15 m (Approx)

Lateral surface area of conical portion = πrl

22/7*2.15*3.04

143.792/7

= 20.5417 m²

⇒ 51.3543 + 20.5417

= 71.896 m²

Volume of Cylindrical portion = πr²h

22/7*2.15*2.15*3.8

386.441/7

= 55.2059 m³

Volume of the conical portion = 1/3πr²h

1/3*22/7*2.15*2.15*2.15

218.64425/21

= 10.4116 m³

Total volume of the building =

55.2059 + 10.4116

= 65.6175 m³

Answer 2

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