1. Problem: Find the height of a cone with radius 6 cm and volume 301.44 cm³. The volume formula for a cone is $$V=\frac{1}{3}\pi r^2 h$$. Given $V=301.44$ and $r=6$, substitute: $$301.44=\frac{1}{3}\pi (6)^2 h=\frac{1}{3}\pi 36 h=12\pi h$$ Solve for $h$: $$h=\frac{301.44}{12\pi}$$ Calculate: $$h=\frac{301.44}{37.6991}\approx 8$$ cm. 2. Problem: Find the height of a cone with radius 4 cm and volume 100.48 cm³. Using the same formula: $$100.48=\frac{1}{3}\pi (4)^2 h=\frac{1}{3}\pi 16 h=\frac{16\pi}{3} h$$ Solve for $h$: $$h=\frac{100.48}{\frac{16\pi}{3}}=\frac{100.48 \times 3}{16\pi}$$ Calculate: $$h=\frac{301.44}{50.2655}\approx 6$$ cm. 3. Problem: Find the radius of a cone with volume 376.8 cm³ and height 12 cm. Volume formula: $$376.8=\frac{1}{3}\pi r^2 (12)=4\pi r^2$$ Solve for $r^2$: $$r^2=\frac{376.8}{4\pi}=\frac{376.8}{12.5664}\approx 30$$ Find $r$: $$r=\sqrt{30}\approx 5.48$$ cm. 4. Problem: Find the radius of a cone with volume 150.72 cm³ and height 7 cm. Volume formula: $$150.72=\frac{1}{3}\pi r^2 (7)=\frac{7\pi}{3} r^2$$ Solve for $r^2$: $$r^2=\frac{150.72}{\frac{7\pi}{3}}=\frac{150.72 \times 3}{7\pi}$$ Calculate: $$r^2=\frac{452.16}{21.9911}\approx 20.56$$ Find $r$: $$r=\sqrt{20.56}\approx 4.54$$ cm. 5. Problem: Find the radius of a sphere with volume 904.32 cm³. Volume formula for a sphere: $$V=\frac{4}{3}\pi r^3$$ Given $V=904.32$: $$904.32=\frac{4}{3}\pi r^3$$ Solve for $r^3$: $$r^3=\frac{904.32 \times 3}{4\pi}=\frac{2712.96}{12.5664}\approx 216$$ Find $r$: $$r=\sqrt[3]{216}=6$$ cm. 6. Problem: Find the radius of a sphere with volume 268.08 m³. Using the same formula: $$268.08=\frac{4}{3}\pi r^3$$ Solve for $r^3$: $$r^3=\frac{268.08 \times 3}{4\pi}=\frac{804.24}{12.5664}\approx 64$$ Find $r$: $$r=\sqrt[3]{64}=4$$ m.