Surface du secteur = (1/4) × 153,86 = 38,465 cm² - Crosslake
Understanding Surface Area Calculation: Surface du Secteur avec Formule Simple
Understanding Surface Area Calculation: Surface du Secteur avec Formule Simple
When working with geometry, understanding surface area is essential—whether for architecture, interior design, or manufacturing. One common calculation involves determining the surface area of a sector, such as a curved surface or segmental portion, using a precise formula. In this article, we explore the scenario Surface du secteur = (1/4) × 153,86 = 38,465 cm², breaking down how this calculation works and why it matters.
What Is Surface du Secteur?
Understanding the Context
The term Surface du secteur refers to the total area of a sector-shaped surface—commonly used in conical, cylindrical, or circular segment geometries. Unlike full surface area calculations, sector surface area focuses on a portion of the curved surface, often expressed as a fraction of the full area.
The Formula Behind Surface du Secteur
The calculation often follows a proportional approach:
> Surface du secteur = (Fraction × Total Area)
Key Insights
In this specific example:
- Fraction = 1/4 (meaning 25% of the full surface area)
- Total given area = 153,86 cm²
Applying the formula:
Surface du secteur = (1/4) × 153,86 = 38,465 cm²
This value represents exactly 25% of the total surface area, making it useful in practical applications where partial coverage or segmental sections are analyzed.
Real-World Applications
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📰 Solution: Let $ h(x) = ax^2 + bx + c $. From $ h(1) = a + b + c = 5 $ and $ h(-1) = a - b + c = 3 $, adding gives $ 2a + 2c = 8 $, so $ a + c = 4 $. The sum of roots is $ - rac{b}{a} = 4 $, so $ b = -4a $. Substituting $ b = -4a $ into $ a + b + c = 5 $: $ a - 4a + c = 5 $ â $ -3a + c = 5 $. Since $ a + c = 4 $, subtracting gives $ -4a = 1 $, so $ a = - rac{1}{4} $. Then $ c = 4 - a = 4 + rac{1}{4} = rac{17}{4} $, and $ b = -4a = 1 $. Thus, $ h(x) = - rac{1}{4}x^2 + x + rac{17}{4} $. Multiplying by 4 to eliminate fractions: $ h(x) = -x^2 + 4x + 17 $. Verifying $ h(1) = -1 + 4 + 17 = 20 $? Wait, inconsistency. Rechecking: $ a = -1/4 $, $ c = 17/4 $, $ b = 1 $. Then $ h(1) = -1/4 + 1 + 17/4 = (-1 + 4 + 17)/4 = 20/4 = 5 $, correct. $ h(-1) = -1/4 -1 + 17/4 = ( -1 -4 + 17 )/4 = 12/4 = 3 $, correct. Sum of roots $ -b/a = -1 / (-1/4) = 4 $, correct. Final answer: $ oxed{-x^2 + 4x + \dfrac{17}{4}} $ or $ oxed{-\dfrac{1}{4}x^2 + x + \dfrac{17}{4}} $. 📰 Question: A science communicator observes that the number of views $ V(t) $ on a video grows quadratically over time $ t $ (in days). If $ V(1) = 120 $, $ V(2) = 200 $, and $ V(3) = 300 $, find $ V(4) $. 📰 Solution: Assume $ V(t) = at^2 + bt + c $. From $ V(1) = a + b + c = 120 $, $ V(2) = 4a + 2b + c = 200 $, $ V(3) = 9a + 3b + c = 300 $. Subtract first equation from the second: $ 3a + b = 80 $. Subtract second from the third: $ 5a + b = 100 $. Subtract these: $ 2a = 20 $ â $ a = 10 $. Then $ 3(10) + b = 80 $ â $ b = 50 $. From $ a + b + c = 120 $: $ 10 + 50 + c = 120 $ â $ c = 60 $. Thus, $ V(t) = 10t^2 + 50t + 60 $. For $ t = 4 $: $ V(4) = 10(16) + 50(4) + 60 = 160 + 200 + 60 = 420 $. Final answer: $ oxed{420} $.Final Thoughts
Calculating surface du secteur is vital in numerous fields:
- Architecture: Estimating tiled or painted curved surfaces like domes or curved walls.
- Manufacturing: Determining material needs for cylindrical or tapered components.
- Estate Planning: Calculating landscaping or paved areas shaped as sectors.
- Design: Creating precise models for manufacturers or product designers.
Why This Calculation Matters
Using simple fractions like 1/4 streamlines complex spatial planning, ensuring accurate material estimates, cost estimation, and resource allocation. It also supports efficient space utilization—especially when only partial coverage is required.
Final Thought
Mastering the surface du secteur formula empowers you to handle more precise geometric calculations with confidence. By understanding how to compute Surface du secteur = (1/4) × 153,86 = 38,465 cm², professionals and hobbyists alike can tackle real-world spatial challenges efficiently and accurately.
Keywords: surface du secteur, surface calculation, fraction area formula, 153,86 cm², curved surface area, geometric formulas, practical geometry, surface area calculation.
If you’re working on projects involving sectors or curved surfaces, leverage this simple yet powerful calculation to enhance accuracy and efficiency.
