Question

The approximate surface area of a sphere of radius \(2.01\) cm is

• A. \(16.16\pi \ \text{cm}^{2}\)
• B. \(16.15\pi \ \text{cm}^{2}\)
• C. \(16.14\pi \ \text{cm}^{2}\)
• D. \(16.17\pi \ \text{cm}^{2}\)

Hint:

Use dS = 8 pi r dr with r = 2 and dr = 0.01 and add it to the exact area at r = 2.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
The surface area is \(S=4\pi r^{2}\), so \(dS=8\pi r\,dr\).

Step 2: Choose values
Take \(r=2\) and \(dr=0.01\).

Step 3: Calculate
\(S(2)=16\pi\) and \(dS=8\pi (2)(0.01)=0.16\pi\).

Step 4: Add
\(S(2.01)\approx 16\pi +0.16\pi =16.16\pi \ \text{cm}^{2}\).

Final Answer:
The approximate area is \(16.16\pi\ \text{cm}^{2}\). \[ \boxed{\text{(A) }16.16\pi \ \text{cm}^{2}} \]