1. **Problem:** Calculate the product of the numbers in standard notation: $$(3.2 \times 10^{-5}) \times (2.5 \times 10^{3})$$ Step 1: Multiply the decimal parts: $$3.2 \times 2.5 = 8.0$$ Step 2: Add the exponents of 10: $$-5 + 3 = -2$$ Step 3: Combine the results: $$8.0 \times 10^{-2}$$ Step 4: Express in the form given in options. Note that $$8.0 \times 10^{-2} = 0.08 = 0.8 \times 10^{-1}$$ **Answer:** A. $0.8 \times 10^{-1}$ 2. **Problem:** Find the cross-sectional area of a cylinder with diameter 6 cm. Step 1: Calculate the radius: $$r = \frac{6}{2} = 3 \text{ cm}$$ Step 2: Use the formula for the area of a circle: $$A = \pi r^2$$ Step 3: Substitute the radius: $$A = \pi \times 3^2 = 9\pi \text{ cm}^2$$ **Answer:** B. $9\pi$ cm$^2$ 3. **Problem:** Find the volume of the cylinder with diameter 6 cm and height 15 cm. Step 1: Use the radius from previous step: $$r = 3 \text{ cm}$$ Step 2: Use the formula for volume of a cylinder: $$V = \pi r^2 h$$ Step 3: Substitute values: $$V = \pi \times 3^2 \times 15 = 135\pi \text{ cm}^3$$ **Answer:** D. $135\pi$ cm$^3$