The equation given is:

\[
4050 = -700 + r^3
\]

To solve for \( r \), follow these steps:

### Step 1: Isolate \( r^3 \)
Add 700 to both sides of the equation:

\[
4050 + 700 = r^3
\]

\[
4750 = r^3
\]

### Step 2: Solve for \( r \)
Take the cube root of both sides to solve for \( r \):

\[
r = \sqrt[3]{4750}
\]

Using a calculator to find the cube root:

\[
r \approx 17.82
\]

Thus, \( r \approx 17.82 \).

Would you like more details or have any other questions?

Here are 5 related questions to explore:
1. What is the general method for solving cubic equations?
2. How can you approximate cube roots without a calculator?
3. What are the applications of cube roots in real-world problems?
4. How do cube roots behave differently from square roots?
5. How can you express large numbers like 4750 as powers of simpler numbers?

**Tip**: Always check your result by plugging it back into the original equation!

Learn how to solve the equation 4050 = -700 + r^3 by isolating r^3 and calculating the cube root. This problem involves key algebraic concepts, such as equations and cube roots, suitable for students in Grades 9-12.

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4050

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