1. **Volume of spherical ball is 4846.59 cm³, radius 10.5 cm. True or False?** Volume of sphere formula: $$ V = \frac{4}{3}\pi r^3 $$ Calculate volume with $r=10.5$: $$ V = \frac{4}{3} \times \pi \times (10.5)^3 = \frac{4}{3} \times 3.1416 \times 1157.625 = 4841.44 \text{ cm}^3 $$ Given volume is 4846.59 cm³, close enough considering rounding. So, **TRUE**. 2. **Volume of cylinder radius 7 cm, height 12 cm is 263.76 cm². True or False?** Volume of cylinder formula: $$ V = \pi r^2 h $$ Calculate: $$ V = 3.1416 \times 7^2 \times 12 = 3.1416 \times 49 \times 12 = 1846.56 \text{ cm}^3 $$ Given units are cm² (area), but volume in cm³. Given number is wrong and unit wrong. **FALSE**. 3. **Area of base of cone is 4.5 m, height 3.5 m. Volume is 18.54 m³. True or False?** Volume of cone formula: $$ V = \frac{1}{3} \times (\text{base area}) \times h $$ Calculate: $$ V = \frac{1}{3} \times 4.5 \times 3.5 = 5.25 \text{ m}^3 $$ Given is 18.54 m³, so **FALSE**. 4. **Volume of sphere is 2143.58 cm³ with diameter 8 cm. True or False?** $r = 4$ cm $$ V = \frac{4}{3} \pi (4)^3 = \frac{4}{3} \times 3.1416 \times 64 = 268.08 \text{ cm}^3 $$ Given volume is 2143.58 cm³, too big, so **FALSE**. 5. **Volume of cone is 100.6 cm³, $r=4$ cm, $h=6$ cm. True or False?** Calculate volume: $$ V = \frac{1}{3} \times \pi \times 4^2 \times 6 = \frac{1}{3} \times 3.1416 \times 16 \times 6 = 100.53 \text{ cm}^3 $$ Given 100.6 close enough, so **TRUE**. 6. **Ball radius 3.5 m, volume 179.50 m³. True or False?** Calculate volume: $$ V = \frac{4}{3} \pi \times 3.5^3 = \frac{4}{3} \times 3.1416 \times 42.875 = 179.59 \text{ m}^3 $$ Given 179.50 close enough, so **TRUE**. 7. **Volume is measured in square units, meaning it tells how many cubes fill the figure. True or False?** Volume is in cubic units, not square units. **FALSE**. 8. **Sphere’s volume solved same way as cone’s volume. True or False?** Volume formulas differ. **FALSE**. 9. **Formula volume of sphere is $\frac{3}{4}$ radius cubed. True or False?** Correct formula: $$ V = \frac{4}{3} \pi r^3 $$ **FALSE**. 10. **Formula volume of cone is $\frac{1}{3}$ base area times height. True or False?** Correct. **TRUE**. --- **Problem 1: Find height of cone with $r=4$ ft, volume approx 165 ft³** Use formula: $$ V = \frac{1}{3} \pi r^2 h $$ Given $V=165$, solve for $h$: $$ h = \frac{3V}{\pi r^2} = \frac{3 \times 165}{3.1416 \times 16} = \frac{495}{50.265} = 9.84 \text{ ft} $$ **Problem 2: Ice cream cone diameter 3 in, height 5 in. Find volume.** Radius $r=1.5$ in. $$ V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.1416 \times (1.5)^2 \times 5 = \frac{1}{3} \times 3.1416 \times 2.25 \times 5 = 11.78 \text{ in}^3 $$ **Problem 3: Luigi’s cone hat, diameter 19 in, height 7.5 in, find volume.** Radius $r=9.5$ in. $$ V= \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.1416 \times (9.5)^2 \times 7.5 = \frac{1}{3} \times 3.1416 \times 90.25 \times 7.5 = 707.54 \text{ in}^3 $$ **Problem 4: Ball radius 8.4 cm, find volume. Round to hundredth** $$ V= \frac{4}{3} \pi (8.4)^3 = \frac{4}{3} \times 3.1416 \times 592.7 = 2483.61 \text{ cm}^3 $$