Find the Area of the Surface Obtained by Rotating the Curve

question 75

Multiple Choice

Find the area of the surface obtained by rotating the curve about the x-axis. $x=\frac{1}{3}\left(y^{2}+2\right) ^{\frac{3}{2}}, 1 \leq y \leq 4$

• A) \(\frac{285}{2}\) \(\pi\)
• B) \(283\) \(\pi\)
• C) \(281\) \(\pi\)
• D) \(\frac{287 \pi}{2}\)
• E) \(\frac{289 \pi}{2}\)

---

Definitions:

Heterozygous

Having two different alleles of a particular gene, one inherited from each parent, resulting in variation of a specific genetic trait.

Nutrient Absorption

The process by which substances such as vitamins, minerals, and other food components are taken up and assimilated into the body, typically occurring in the intestines.

Hypha

One of the threadlike filaments composing the mycelium of a water mold or fungus.

Fruiting Body

The spore-producing structure of fungi and other plants which is usually seen above ground.