To find the new surface area of the cylinder after dilation, we first need to determine the new dimensions after applying the scale factor of 4.
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Original dimensions:
- Height (h) = 15 cm
- Radius (r) = 8 cm
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New dimensions after dilation:
- New height = 4 * 15 cm = 60 cm
- New radius = 4 * 8 cm = 32 cm
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Surface area formula for a cylinder: \[ SA = 2\pi rh + 2\pi r^2 \]
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Calculating the new surface area: Substitute the new height and radius into the formula: \[ SA = 2\pi (32)(60) + 2\pi (32^2) \]
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Calculate \( 2\pi (32)(60) \): \[ 2\pi (32)(60) = 3840\pi , \text{cm}^2 \]
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Calculate \( 2\pi (32^2) \): \[ 32^2 = 1024 \implies 2\pi (1024) = 2048\pi , \text{cm}^2 \]
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Now add them together: \[ SA = 3840\pi + 2048\pi = 5888\pi , \text{cm}^2 \]
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Therefore, the new surface area of the dilated cylinder is 5,888π cm².