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Les cylindres suivants sont semblables. Quelle est la hauteur du petit cylindre? A_(T)=37,7dm^(2) A_(T)=603,19dm^(2)

Les cylindres suivants sont semblables. Quelle est la hauteur du petit cylindre?\newlineAT=37,7dm2 A_{T}=37,7 \mathrm{dm}^{2} \newlineAT=603,19dm2 A_{T}=603,19 \mathrm{dm}^{2}

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Q. Les cylindres suivants sont semblables. Quelle est la hauteur du petit cylindre?\newlineAT=37,7dm2 A_{T}=37,7 \mathrm{dm}^{2} \newlineAT=603,19dm2 A_{T}=603,19 \mathrm{dm}^{2}
  1. Calculate Area Ratio: Since the cylinders are similar, the ratio of their areas is the square of the ratio of their heights.\newlineLet h1h_1 be the height of the smaller cylinder and h2h_2 be the height of the larger cylinder.\newlineWe have AT1=37.7 dm2A_{T1} = 37.7 \, \text{dm}^2 for the smaller cylinder and AT2=603.19 dm2A_{T2} = 603.19 \, \text{dm}^2 for the larger cylinder.
  2. Find Height Ratio: Calculate the ratio of the areas.\newlineratio = AT1/AT2=37.7/603.19A_{T1} / A_{T2} = 37.7 / 603.19
  3. Calculate Square Root: Perform the division to find the ratio.\newlineratio = 37.7603.19≈0.0625\frac{37.7}{603.19} \approx 0.0625
  4. Calculate Height Ratio: Since the ratio of the areas is the square of the ratio of the heights, take the square root of the ratio to find the ratio of the heights.\newlineheight_ratio=ratio=0.0625\text{height\_ratio} = \sqrt{\text{ratio}} = \sqrt{0.0625}
  5. Calculate Square Root: Calculate the square root.\newlineheight_ratio=0.0625=0.25height\_ratio = \sqrt{0.0625} = 0.25
  6. Determine Height: If the height of the larger cylinder is not given, we cannot determine the height of the smaller cylinder with the information provided.

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