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.
Answers
Answer:
The Internal curved surface area of the building is 735.43 m² and Capacity of a building is 2112 m³.
Step-by-step explanation:
SOLUTION :
Given :
Radius of the cylinder and cone, r = 12 m
Height of the cylinder,H = 3.5 m
slant height of the cone , l = 12.5 m
Height of the right cone , h = √l² - r²
h = √12.5² - 12²
h = √(156.25 - 144)
h = √12.25
h = 3.5 m
Height of the cone,h = 3.5 m.
Capacity of a building ,V = Volume(Capacity) of a cylinder + Volume (Capacity) of a cone
V = πr²H + 1/3πr²h
V = πr²(H + ⅓ h)
V = 22/7 × 12² × (3.5 + ⅓ × 3.5)
V = 22/7 × 144 × 3.5 (1 + ⅓)
V = 22 × 144 × 0.5 × 4/3
V = 22× 48 × 2
V = 44 × 48
V = 2112 m³
Capacity of a building = 2112 m³
Internal curved surface area of the building = Curved surface area of the cylinder + Curved surface area of the cone
= 2πrh + πrl
= πr(2h + l)
= π ×12 × (2 × 3.5 + 12.5)
= π × 12(7 + 12.5)
= 22/7 × 12 × 19.5
= 5148/7
= 735.43 m²
Internal curved surface area of the building = 735.43 m²
Hence, Internal curved surface area of the building is 735.43 m² and Capacity of a building is 2112 m³.
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Answer:
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