Find the volume and surface area of a sphere of radius 21 cm.

Answer

To find the volume and surface area of a sphere with a radius of 21 cm, we will follow these steps:

### Step 1: Identify the formulas
The formulas we need are:
- Volume of a sphere: \( V = \frac{4}{3} \pi r^3 \)
- Surface area of a sphere: \( A = 4 \pi r^2 \)

### Step 2: Substitute the radius into the volume formula
Given the radius \( r = 21 \) cm, we substitute this value into the volume formula:
\[ V = \frac{4}{3} \pi (21)^3 \]

### Step 3: Calculate \( r^3 \)
First, we calculate \( 21^3 \):
\[ 21^3 = 21 \times 21 \times 21 = 441 \times 21 = 9261 \]

### Step 4: Substitute \( r^3 \) back into the volume formula
Now, substituting \( 9261 \) into the volume formula:
\[ V = \frac{4}{3} \pi (9261) \]

### Step 5: Calculate the volume
Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{4}{3} \times \frac{22}{7} \times 9261 \]
Calculating \( \frac{4 \times 22 \times 9261}{3 \times 7} \):
1. Calculate \( 4 \times 22 = 88 \)
2. Now calculate \( 88 \times 9261 = 815868 \)
3. Finally, divide by \( 21 \) (since \( 3 \times 7 = 21 \)):
\[ V = \frac{815868}{21} = 38808 \text{ cm}^3 \]

### Step 6: Substitute the radius into the surface area formula
Now, we calculate the surface area:
\[ A = 4 \pi (21)^2 \]

### Step 7: Calculate \( r^2 \)
Calculate \( 21^2 \):
\[ 21^2 = 441 \]

### Step 8: Substitute \( r^2 \) back into the surface area formula
Now substituting \( 441 \) into the surface area formula:
\[ A = 4 \pi (441) \]

### Step 9: Calculate the surface area
Using \( \pi \approx \frac{22}{7} \):
\[ A = 4 \times \frac{22}{7} \times 441 \]
Calculating \( 4 \times 22 = 88 \):
\[ A = \frac{88 \times 441}{7} \]
Calculating \( 88 \times 441 = 38768 \):
\[ A = \frac{38768}{7} = 5544 \text{ cm}^2 \]

### Final Answers
- Volume of the sphere: \( 38808 \text{ cm}^3 \)
- Surface area of the sphere: \( 5544 \text{ cm}^2 \)