The largest four digit number which is a perfect cube, is

Options

A. 9999
B. 9261
C. 8000
D. None

Answer

To find the largest four-digit number that is a perfect cube, we can follow these steps:

### Step 1: Identify the range of four-digit numbers
The smallest four-digit number is 1000, and the largest four-digit number is 9999.

### Step 2: Find the cube root of the largest four-digit number
To determine the largest perfect cube within the four-digit range, we need to find the cube root of 9999.

\[ \sqrt[3]{9999} \approx 21.544 \]

### Step 3: Determine the largest integer less than or equal to the cube root
The largest integer less than or equal to 21.544 is 21. Therefore, we will calculate \(21^3\) to find the largest perfect cube.

### Step 4: Calculate \(21^3\)
Now we compute \(21^3\):

\[ 21^3 = 21 \times 21 \times 21 \]
Calculating step-by-step:
- First, calculate \(21 \times 21 = 441\).
- Next, multiply \(441 \times 21\):

\[ 441 \times 21 = 441 \times (20 + 1) = 441 \times 20 + 441 \times 1 = 8820 + 441 = 9261 \]

### Step 5: Conclusion
The largest four-digit number which is a perfect cube is:

\[ \boxed{9261} \]

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