1. **Find the volume of the triangular prism.** The formula for the volume of a prism is: $$V = B \times h$$ where $B$ is the area of the base and $h$ is the height (length) of the prism. For a triangular base, the area is: $$B = \frac{1}{2} \times \text{base} \times \text{height}$$ Given: - Triangle legs: 6 cm and 8 cm (right triangle) - Prism length (height): 12 cm Calculate the base area: $$B = \frac{1}{2} \times 6 \times 8 = \frac{1}{2} \times 48 = 24 \text{ cm}^2$$ Calculate the volume: $$V = 24 \times 12 = 288 \text{ cm}^3$$ --- 2. **Find the volume of the cylinder with radius 8 in and height 17 in.** The formula for the volume of a cylinder is: $$V = \pi r^2 h$$ Given: - Radius $r = 8$ in - Height $h = 17$ in Calculate the volume: $$V = \pi \times 8^2 \times 17 = \pi \times 64 \times 17 = 1088\pi \approx 3417.3 \text{ in}^3$$ --- 3. **Find the volume of the cylinder with diameter 15 mm and height 18 mm.** First, find the radius: $$r = \frac{15}{2} = 7.5 \text{ mm}$$ Use the volume formula: $$V = \pi r^2 h = \pi \times 7.5^2 \times 18 = \pi \times 56.25 \times 18 = 1012.5\pi \approx 3180.2 \text{ mm}^3$$ --- **Final answers:** 1. Volume of triangular prism = $288$ cm$^3$ 2. Volume of cylinder (8 in radius) = $3417.3$ in$^3$ 3. Volume of cylinder (15 mm diameter) = $3180.2$ mm$^3$