  Write an expression for the surface area of the sphere in terms of x.  Hint:plug x/3 in the equation for r and simplify.
*
3 points
Captionless Image

A.

B.

C.

D.

The surface area \( A \) of a sphere is given by the formula:

\[
A = 4\pi r^2
\]

According to the hint, we are to substitute \( \frac{x}{3} \) for \( r \). So, replace \( r \) in the formula with \( \frac{x}{3} \):

\[
A = 4\pi \left( \frac{x}{3} \right)^2
\]

Now, simplify the expression:

\[
A = 4\pi \left( \frac{x^2}{9} \right)
\]

\[
A = \frac{4\pi x^2}{9}
\]

Thus, the expression for the surface area in terms of \( x \) is:

\[
A = \frac{4\pi x^2}{9}
\]

Let me know if you want more details or have any questions! Here are 5 related questions:

1. What is the volume formula of a sphere in terms of \( x \) if \( r = \frac{x}{3} \)?
2. How do you derive the surface area formula for a

Write an expression for the surface area of the sphere in terms of x. Hint: plug x/3 in the equation for r and simplify.

Learn how to find the surface area of a sphere by substituting x/3 for the radius. This problem focuses on the formula for surface area, A = 4πr^2, and shows how to simplify it step-by-step to express it in terms of x. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation