1. **Problem statement:** Find the volumes of the given 3D shapes to 1 decimal place. 2. **Formulas:** - Volume of a cone: $$V=\frac{1}{3}\pi r^2 h$$ where $r$ is radius and $h$ is height. - Volume of a pyramid: $$V=\frac{1}{3} \times \text{base area} \times h$$ - Volume of a triangular prism (or pyramid-like solid): $$V=\frac{1}{2} \times \text{base} \times \text{height of triangle} \times \text{length}$$ - Volume of a sphere: $$V=\frac{4}{3}\pi r^3$$ - Volume of a hemisphere: $$V=\frac{1}{2} \times \frac{4}{3}\pi r^3=\frac{2}{3}\pi r^3$$ 3. **Calculations:** **Top-left cone:** diameter = 10 cm, so radius $r=\frac{10}{2}=5$ cm, height $h=11$ cm. $$V=\frac{1}{3}\pi (5)^2 (11)=\frac{1}{3}\pi 25 \times 11=\frac{275}{3}\pi$$ $$V\approx \frac{275}{3} \times 3.1416=287.98 \approx 288.0 \text{ cm}^3$$ **Top-right cone:** diameter = 5 cm, radius $r=\frac{5}{2}=2.5$ cm, height $h=15$ cm. $$V=\frac{1}{3}\pi (2.5)^2 (15)=\frac{1}{3}\pi 6.25 \times 15=\frac{93.75}{3}\pi=31.25\pi$$ $$V\approx 31.25 \times 3.1416=98.17 \approx 98.2 \text{ cm}^3$$ **Center-right pyramid:** base dimensions 9 cm by 5 cm, height $h=10$ cm. Base area = $9 \times 5=45$ cm$^2$. $$V=\frac{1}{3} \times 45 \times 10=150 \text{ cm}^3$$ **Bottom-left triangular pyramid/prism-like solid:** dimensions 7 cm, 5 cm, 6 cm. Assuming base is triangle with base=7 cm, height=5 cm, length=6 cm. Volume: $$V=\frac{1}{2} \times 7 \times 5 \times 6=\frac{1}{2} \times 35 \times 6=17.5 \times 6=105 \text{ cm}^3$$ **Center sphere:** radius $r=5.5$ cm. $$V=\frac{4}{3}\pi (5.5)^3=\frac{4}{3}\pi 166.375=\frac{665.5}{3}\pi$$ $$V\approx 221.83 \times 3.1416=696.91 \approx 696.9 \text{ cm}^3$$ **Bottom-right hemisphere:** diameter = 7 cm, radius $r=\frac{7}{2}=3.5$ cm. $$V=\frac{2}{3}\pi (3.5)^3=\frac{2}{3}\pi 42.875=\frac{85.75}{3}\pi$$ $$V\approx 28.58 \times 3.1416=89.77 \approx 89.8 \text{ cm}^3$$ 4. **Final answers:** - Top-left cone: $288.0$ cm$^3$ - Top-right cone: $98.2$ cm$^3$ - Center-right pyramid: $150.0$ cm$^3$ - Bottom-left triangular pyramid/prism: $105.0$ cm$^3$ - Center sphere: $696.9$ cm$^3$ - Bottom-right hemisphere: $89.8$ cm$^3$