How many cups does a $$ 12^{\prime \prime} $$ hemispherical bowl hold? 1 cup is approximately 14.4 cubic inches. About 5 cups About 75 cups About 452 cups About 31 cups QuEstion 4 You needed to paint a ceramic bowl with a $$ 6^{\prime \prime} $$ diameter. How much square inches of paint will you use? $$ 84.8 \mathrm{in}^{2} $$ $$ 169.6 \mathrm{in}^{2} $$ $$ 18.8 \mathrm{in}^{2} $$ $$ 56.5 \mathrm{in}^{2} $$

Question

UpStudy AI · Accepted Answer

Let's address each question step by step.

---

### **Question 3**

**How many cups does a $$ 12'' $$ hemispherical bowl hold?  
1 cup is approximately 14.4 cubic inches.**

**Options:**
- About 5 cups
- About 75 cups
- About 452 cups
- **About 31 cups**

**Solution:**

1. **Calculate the Volume of the Hemisphere:**
   
   - **Diameter (d)** = 12 inches  
   - **Radius (r)** = d/2 = 6 inches  
   
   - **Volume of a Hemisphere (V)** = $$ \frac{2}{3} \pi r^3 $$  
     $$ V = \frac{2}{3} 	imes \pi 	imes 6^3 $$  
     $$ V = \frac{2}{3} 	imes \pi 	imes 216 $$  
     $$ V = 144\pi $$ cubic inches  
     $$ V \approx 452.39 $$ cubic inches

2. **Convert Cubic Inches to Cups:**
   
   - **1 cup** ≈ 14.4 cubic inches  
   
   - **Number of Cups** = $$ \frac{452.39}{14.4} $$  
     $$ \approx 31.39 $$ cups

**Answer:** **About 31 cups**

---

### **Question 4**

**You needed to paint a ceramic bowl with a $$ 6'' $$ diameter. How much square inches of paint will you use?**

**Options:**
- $$ 84.8 \, 	ext{in}^2 $$
- $$ 169.6 \, 	ext{in}^2 $$
- $$ 18.8 \, 	ext{in}^2 $$
- **$$ 56.5 \, 	ext{in}^2 $$**

**Solution:**

1. **Determine Surface Area to Paint:**
   
   - **Diameter (d)** = 6 inches  
   - **Radius (r)** = d/2 = 3 inches  
   
   - **Surface Area of a Hemisphere (excluding base)** = $$ 2\pi r^2 $$  
     $$ = 2 	imes \pi 	imes 3^2 $$  
     $$ = 18\pi $$ square inches  
     $$ \approx 56.55 $$ square inches

**Answer:** **$$ 56.5 \, 	ext{in}^2 $$**

---

**Summary of Answers:**
- **First Question:** About **31 cups**
- **Second Question:** **56.5 square inches**
- **First Question:** About 31 cups - **Second Question:** 56.5 square inches

How many cups does a hemispherical bowl hold? 1 cup is approximately 14.4 cubic inches.
About 5 cups
About 75 cups
About 452 cups
About 31 cups
QuEstion 4
You needed to paint a ceramic bowl with a diameter. How much square inches of paint will you use?

Upstudy AI Solution

Answer

Solution

Question 3

Question 4

Extra Insights

Related Questions

Latest Geometry Questions

How many cups does a hemispherical bowl hold? 1 cup is approximately 14.4 cubic inches. About 5 cups About 75 cups About 452 cups About 31 cups QuEstion 4 You needed to paint a ceramic bowl with a diameter. How much square inches of paint will you use?