The relationship between the radius of a sphere and its surtace area is given by. $$ S A=4 \pi^{2} $$ where SA = surface area and $$ r= $$ radius. 1st attempt Part 1 ( 0.5 point) See Periodic Table The mean radius of the Earth is $$ 6,371 \mathrm{~km} $$, and $$ 70.8 \% $$ of its surface is covered by water. What is the surface area of the Earth covered by land? $$ 109 \quad \times 10^{8} \mathrm{~km}^{2} $$ Part 2 ( 0.5 point) If $$ 167 \mathrm{~cm}^{2} $$ of leather is stitched together to make a baseball, what is the radius of the baseball? $$ \square $$ cm

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UpStudy AI · Accepted Answer

Hello! Let's review and correct your first attempt, and then work through Part 2 together.

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### **Part 1**

**Your Attempt:**
- **Formula Used:** $$ \text{SA} = 4 \pi^{2} $$
- **Given:**
  - Mean radius of Earth, $$ r = 6,371 $$ km
  - Percentage covered by water = $$ 70.8\% $$
- **Your Answer:** $$ 109 \times 10^{8} $$ km²

**Corrections & Solution:**

1. **Correct Surface Area Formula:**
   
   The correct formula for the surface area $$ \text{SA} $$ of a sphere is:
   $$
   \text{SA} = 4 \pi r^{2}
   $$
   *(Note: It seems there was a typo in your formula.)*

2. **Calculate Earth's Surface Area:**
   $$
   \text{SA} = 4 \pi (6,371 \, \text{km})^{2} = 4 \pi (40,589,641 \, \text{km}²) \approx 510 \times 10^{6} \, \text{km}²
   $$
   
3. **Determine Land Area:**
   
   Since $$ 70.8\% $$ is covered by water, $$ 29.2\% $$ is land.
   $$
   \text{Land Area} = 0.292 \times 510 \times 10^{6} \, \text{km}² \approx 149 \times 10^{6} \, \text{km}²
   $$
   
   So, the **correct surface area of the Earth covered by land** is approximately $$ 1.49 \times 10^{8} $$ km² (or $$ 149 \times 10^{6} $$ km²).

**Summary:** It looks like there was a mistake in both the formula and the calculation, leading to an incorrect surface area value. The accurate land area should be around $$ 1.49 \times 10^{8} $$ km².

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### **Part 2**

**Problem:**
If $$ 167 $$ cm² of leather is stitched together to make a baseball, what is the radius of the baseball?

**Solution:**

1. **Surface Area Formula:**
   $$
   \text{SA} = 4 \pi r^{2}
   $$
   
   Given $$ \text{SA} = 167 $$ cm².

2. **Solve for $$ r $$:**
   $$
   4 \pi r^{2} = 167
   $$
   $$
   r^{2} = \frac{167}{4 \pi} \approx \frac{167}{12.566} \approx 13.28
   $$
   $$
   r \approx \sqrt{13.28} \approx 3.65 \, \text{cm}
   $$
   
**Answer:** The radius of the baseball is approximately **3.65 cm**.

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Feel free to ask if you have any more questions or need further clarification!
The surface area of the Earth covered by land is approximately $$ 1.49 \times 10^{8} $$ km². The radius of the baseball is approximately 3.65 cm.

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