1. **Find the total volume of the pyramid on top of the cube:** - Given: Pyramid height $h=8$ cm, cube side length $S=8$ cm. - Volume of pyramid formula: $$V_{pyramid} = \frac{1}{3}Bh$$ where $B$ is the base area. - Since the pyramid is triangular and sits on the cube top, assume base area $B$ equals the cube's top face area: $$B = S^2 = 8^2 = 64 \text{ cm}^2$$ - Calculate pyramid volume: $$V_{pyramid} = \frac{1}{3} \times 64 \times 8 = \frac{512}{3} \approx 170.67 \text{ cm}^3$$ - Volume of cube formula: $$V_{cube} = S^3 = 8^3 = 512 \text{ cm}^3$$ - Total volume (pyramid + cube): $$V_{total} = 512 + \frac{512}{3} = \frac{1536}{3} + \frac{512}{3} = \frac{2048}{3} \approx 682.67 \text{ cm}^3$$ 2. **Find the total volume of the large cylinder with a smaller cylinder cut out:** - Large cylinder radius $r_1=8$ in, height $h=11$ in. - Small cylinder radius $r_2=3$ in, height $h=11$ in. - Volume of large cylinder: $$V_{large} = \pi r_1^2 h = \pi \times 8^2 \times 11 = 704\pi \text{ in}^3$$ - Volume of small cylinder: $$V_{small} = \pi r_2^2 h = \pi \times 3^2 \times 11 = 99\pi \text{ in}^3$$ - Total volume after cutout: $$V_{total} = V_{large} - V_{small} = 704\pi - 99\pi = 605\pi \approx 1900.27 \text{ in}^3$$ 3. **Find the total volume of the hemisphere on top of the cone:** - Hemisphere radius $r=9$ m. - Cone radius $r=9$ m, height $h=9$ m. - Volume of hemisphere: $$V_{hemi} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi \times 9^3 = \frac{2}{3} \pi \times 729 = 486\pi \text{ m}^3$$ - Volume of cone: $$V_{cone} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi \times 9^2 \times 9 = \frac{1}{3} \pi \times 81 \times 9 = 243\pi \text{ m}^3$$ - Total volume: $$V_{total} = 486\pi + 243\pi = 729\pi \approx 2290.22 \text{ m}^3$$