Find the Area of the Surface Generated by Revolving the Curve

question 71

Multiple Choice

Find the area of the surface generated by revolving the curve about the given axis. $x = t , y = 6 t , 0 \leq t \leq 9$
(i) $x$ -axis; (ii) $y$ -axis

• A) (i) \(486 \sqrt { 37 } \pi\); (ii) \(81 \sqrt { 37 } \pi\)
• B) (i) \(324 \sqrt { 82 } \pi\); (ii) \(36 \sqrt { 82 } \pi\)
• C) (i) \(486 \sqrt { 37 } \pi\); (ii) \(36 \sqrt { 37 } \pi\)
• D) (i) \(81 \sqrt { 37 } \pi\); (ii) \(486 \sqrt { 37 } \pi\)
• E) (i) \(324 \sqrt { 37 } \pi\); (ii) \(81 \sqrt { 37 } \pi\)

---

Definitions:

Million Years

A unit of time equal to one thousand thousand (1,000,000) years, often used in geological and paleontological contexts.

CT Scans

Imaging procedures that use computer-processed combinations of many X-ray measurements taken from different angles to produce cross-sectional images of specific areas of a scanned object.

MRI Scans

Medical imaging techniques that use magnetic fields and radio waves to produce detailed images of the body's internal structures, including organs and tissues.

Fossilized Tissue

Organic material from organisms that has been preserved in the geological record.