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The interior of a building is in the form of cylinder of diameter 10m and height 8m, surmounted by a cone whose vertical angle is a right angle.
Then what will be the area of the surface and the volume of the building?​

Sagot :

Answer:

  • Surface Area = 399.4 m²
  • Volume = 1675.5 m³

Step-by-step explanation:

Lateral Surface Area of the Cylindrical Part

  • 2πrh
  • 2 x π x 5 x 8
  • 80 x π
  • 251.3 m²

Slant height of cone

  • √r² + h²
  • √25 + 64
  • √89
  • 9.43 m

Surface Area of Conical Portion

  • πrl
  • π x 5 x 9.43
  • 47.15 x π
  • 148.1 m²

Total Surface Area :

  • 251.3 + 148.1
  • 399.4 m²

Volume

  • V = πr²h + 1/3πr²h
  • V = πr²h (1 + 1/3)
  • V = π x 25 x 8 x (4/3)
  • V = π x 1600/3
  • V = 1675.5 m³
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