Assertion (A) : A solid iron in the form of a cuboid of dimensions `49 cm xx 33 cm xx 24 cm` is melted to form a solid sphere. Then the radius of sphere will be 21 cm.
Reason (R) : Volume of cylinder `= pir^(2)h, r` is the radius of the cylinder and h is the height of the cylinder.

Options

A. Both A and R are true and R is the correct explanation of A.
B. Both A and R are true and R is not the correct explanation of A.
C. A is true but R is false
D. A is false but R is true

Answer

To solve the problem, we need to verify the assertion (A) and the reason (R) provided in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- We have a cuboid with dimensions \(49 \, \text{cm} \times 33 \, \text{cm} \times 24 \, \text{cm}\).
- This cuboid is melted to form a solid sphere.
- We need to check if the radius of the sphere is \(21 \, \text{cm}\).

2. **Calculate the Volume of the Cuboid**:
- The volume \(V\) of a cuboid is given by the formula:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
- Substituting the dimensions:
\[ V = 49 \, \text{cm} \times 33 \, \text{cm} \times 24 \, \text{cm} \]

3. **Perform the Multiplication**:
- First, calculate \(49 \times 33\):
\[ 49 \times 33 = 1617 \]
- Now multiply this result by \(24\):
\[ 1617 \times 24 = 38808 \, \text{cm}^3 \]
- So, the volume of the cuboid is \(38808 \, \text{cm}^3\).

4. **Volume of the Sphere**:
- The volume \(V\) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
- We will set the volume of the cuboid equal to the volume of the sphere:
\[ 38808 = \frac{4}{3} \pi r^3 \]

5. **Substituting \(\pi\)**:
- Using \(\pi \approx \frac{22}{7}\):
\[ 38808 = \frac{4}{3} \times \frac{22}{7} \times r^3 \]

6. **Rearranging the Equation**:
- To isolate \(r^3\), multiply both sides by \(\frac{3 \times 7}{4 \times 22}\):
\[ r^3 = 38808 \times \frac{3 \times 7}{4 \times 22} \]

7. **Calculating \(r^3\)**:
- First, calculate \(4 \times 22 = 88\).
- Now calculate:
\[ r^3 = 38808 \times \frac{21}{88} \]
- Performing the multiplication:
\[ r^3 = \frac{813888}{88} = 9240 \]

8. **Finding \(r\)**:
- Now, take the cube root of \(9240\) to find \(r\):
\[ r = \sqrt[3]{9240} \approx 20.1 \, \text{cm} \]
- This shows that the radius is not \(21 \, \text{cm}\).

9. **Conclusion**:
- The assertion (A) is **false** because the radius of the sphere is approximately \(20.1 \, \text{cm}\), not \(21 \, \text{cm}\).
- The reason (R) is **true**, but it does not explain the assertion.

### Final Answer:
- Assertion (A) is false.
- Reason (R) is true.
- Therefore, the correct answer is that both A and R are true, but R is not the correct explanation of A.