Find the lateral (side) surface area of the cone generated by revolving the line segment y =7x, Osxs7, about the x-axis. Check your answer with the following geometry formula. Lateral surface area = x base circumference x slant height

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Find the lateral (side) surface area of the cone generated by revolving the line segment \( y = \frac{1}{4} x, \, 0 \leq x \leq 7 \), about the x-axis. Check your answer with the following geometry formula.

Lateral surface area \( = \frac{1}{2} \times \text{base circumference} \times \text{slant height} \)

Set up the integral that gives the surface area of the cone.
Transcribed Image Text:Find the lateral (side) surface area of the cone generated by revolving the line segment \( y = \frac{1}{4} x, \, 0 \leq x \leq 7 \), about the x-axis. Check your answer with the following geometry formula. Lateral surface area \( = \frac{1}{2} \times \text{base circumference} \times \text{slant height} \) Set up the integral that gives the surface area of the cone.
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