1. **State the problem:** Calculate the volume of each given 3D shape using the provided dimensions. 2. **Cylinder (a):** Diameter = 80 cm, Height = 150 cm. - Radius $r = \frac{80}{2} = 40$ cm. - Volume formula: $$V = \pi r^2 h$$ - Substitute values: $$V = \pi \times 40^2 \times 150 = \pi \times 1600 \times 150 = 240000\pi \text{ cm}^3$$ 3. **Cone (b):** Height $h = 7$ m, Radius $r = 2$ m. - Volume formula: $$V = \frac{1}{3} \pi r^2 h$$ - Substitute values: $$V = \frac{1}{3} \pi \times 2^2 \times 7 = \frac{1}{3} \pi \times 4 \times 7 = \frac{28}{3}\pi \text{ m}^3$$ 4. **Hemisphere (c):** Radius $r = 10$ cm. - Volume formula: $$V = \frac{2}{3} \pi r^3$$ - Substitute values: $$V = \frac{2}{3} \pi \times 10^3 = \frac{2}{3} \pi \times 1000 = \frac{2000}{3}\pi \text{ cm}^3$$ 5. **Cone (d):** Height $h = 12$ inci, Diameter = 10 inci, so Radius $r = \frac{10}{2} = 5$ inci. - Volume formula: $$V = \frac{1}{3} \pi r^2 h$$ - Substitute values: $$V = \frac{1}{3} \pi \times 5^2 \times 12 = \frac{1}{3} \pi \times 25 \times 12 = 100\pi \text{ inci}^3$$ 6. **Sphere (e):** Diameter = 8.4 m, so Radius $r = \frac{8.4}{2} = 4.2$ m. - Volume formula: $$V = \frac{4}{3} \pi r^3$$ - Substitute values: $$V = \frac{4}{3} \pi \times 4.2^3 = \frac{4}{3} \pi \times 74.088 = 98.784\pi \text{ m}^3$$ 7. **Rectangular prism (f):** Height = 6 dm, Base = 4 dm by 4 dm. - Volume formula: $$V = \text{length} \times \text{width} \times \text{height}$$ - Substitute values: $$V = 4 \times 4 \times 6 = 96 \text{ dm}^3$$ **Final answers:** - Cylinder: $240000\pi$ cm$^3$ - Cone (b): $\frac{28}{3}\pi$ m$^3$ - Hemisphere: $\frac{2000}{3}\pi$ cm$^3$ - Cone (d): $100\pi$ inci$^3$ - Sphere: $98.784\pi$ m$^3$ - Rectangular prism: $96$ dm$^3$