the length of a cinema hall is 20m and breath is 16 m. the sum of the area of floor and flat roof is equal to the areas of four walls .find the height and volume of hall ?
Answers
Given:
- Length of cinema hall = 20 m
- Breadth of cinema hall = 16 m
To find:
- Height and Volume of hall?
Solution:
★ Area of floor and flat roof,
➻ 2 × (l × b)
➻ 2 × (20 × 16)
➻ 2 × 320
➻ 640 m²
★ Now, Finding area of four walls and flat roof,
We know that,
Area of four wall = Curved surface area of hall
Therefore,
Area of four wall = 2(20 + 16)h
➻ 2 × 36 × h
➻ 72h m²
★ According to the Question:
Area of four walls and flat roof is equal to the areas of four walls
Therefore,
➻ 640 = 72h
➻ h = 640/72
➻ h = 8.8888889
➻ h ≈ 8.889 m
Hence, Height of hall is 8.889 m (approx) .
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• Volume of hall cinema hall,
We know that,
Cinema hall is in cuboidal shape.
Volume of cuboid = l × b × h
Here,
- Length, l = 20 m
- Breadth, b = 16 m
- Height, h = 8.889 m
Putting values,
➻ 20 × 16 × 8.889
➻ 2844.48 m³
Hence, Volume of cinema hall is 2844.48 m³ (approx).
Step-by-step explanation:
Let the height of the wall = h metres Length of the hall (l) = 20 m Width of the hall (b) = 16m Area of the floor = Length × Width = 20 × 16 = 320 cm2 Area of the roof = Area of the floor = 320 cm2 Area of 4 walls = 2 (lh + bh) = 2h (l +b) = 2h (20 + 16) = 72h cm2 By the problem: Area (floor + roof) = area of 4 walls ⇒ 320 + 320 = 72h ⇒ 640 = 72 h ⇒ 8.88 = h ∴ Height of the the wall = 8.88 cm
volume= 20×16×8.88
= 2844.48 cm²
hope it helps
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