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? \( 84.8 \mathrm{in}^{2} \) \( 169.6 \mathrm{in}^{2} \) \( 18.8 \mathrm{in}^{2} \) \( 56.5 \mathrm{in}^{2} \)

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)** = \( \frac{2}{3} \pi r^3 \) \( V = \frac{2}{3} \times \pi \times 6^3 \) \( V = \frac{2}{3} \times \pi \times 216 \) \( V = 144\pi \) 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:** - \( 84.8 \, \text{in}^2 \) - \( 169.6 \, \text{in}^2 \) - \( 18.8 \, \text{in}^2 \) - **\( 56.5 \, \text{in}^2 \)** **Solution:** 1. **Determine Surface Area to Paint:** - **Diameter (d)** = 6 inches - **Radius (r)** = d/2 = 3 inches - **Surface Area of a Hemisphere (excluding base)** = \( 2\pi r^2 \) \( = 2 \times \pi \times 3^2 \) \( = 18\pi \) square inches \( \approx 56.55 \) square inches **Answer:** **\( 56.5 \, \text{in}^2 \)** --- **Summary of Answers:** - **First Question:** About **31 cups** - **Second Question:** **56.5 square inches**