Find the Area of the Surface Generated by Revolving the Curve

question 86

Multiple Choice

Find the area of the surface generated by revolving the curve about the x-axis. $$y = 4 \sqrt { x } , 1 \leq x \leq 7$$

• A) \(\frac { 1 } { 3 } \left( 44 ^ { \frac { 3 } { 2 } } - 20 ^ { \frac { 3 } { 2 } } \right) \pi\)
• B) \(\frac { 2 } { 3 } \left( 32 ^ { \frac { 3 } { 2 } } - 8 ^ { \frac { 3 } { 2 } } \right) \pi\)
• C) \(\frac { 1 } { 3 } \left( 32 ^ { \frac { 3 } { 2 } } - 8 ^ { \frac { 3 } { 2 } } \right) \pi\)
• D) \(\frac { 2 } { 3 } \left( 44 ^ { \frac { 3 } { 2 } } - 20 ^ { \frac { 3 } { 2 } } \right) \pi\)
• E) \(\frac { 1 } { 6 } \left( 32 ^ { \frac { 3 } { 2 } } - 8 ^ { \frac { 3 } { 2 } } \right) \pi\)

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Definitions:

Substage

In microscopy, a component part of the microscope's stage that allows for adjustments, such as altering the intensity of light, to enhance the visualization of specimens.

Shutter or Diaphragm

Mechanical device in a camera that controls the duration and amount of light that reaches the film or sensor, crucial for exposure.

Ocular Lens

A lens located in the eye that focuses light rays onto the retina, enabling vision.

Stage

Has two clips that hold the specimen slide to be viewed.