Subjects geometry

Volume Calculation 25Fb8E

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1. The problem asks to find the volume (rumfanget) of various solids given their height $h$ and base area $G$. 2. The formula for the volume depends on the type of solid: - For prisms and cuboids: $$V = G \times h$$ - For pyramids and cones: $$V = \frac{1}{3} G \times h$$ 3. We apply the correct formula to each solid: **Top-left: Blue rectangular prism/cuboid** - $h = 11$, $G = 17$ cm$^2$ - Volume: $$V = 17 \times 11 = 187 \text{ cm}^3$$ **Top-center: Green triangular pyramid** - $h = 20$, $G = 13$ cm$^2$ - Volume: $$V = \frac{1}{3} \times 13 \times 20 = \frac{260}{3} = 86.67 \text{ cm}^3$$ **Top-right: Red pyramid** - $h = 17$, $G = 29$ cm$^2$ - Volume: $$V = \frac{1}{3} \times 29 \times 17 = \frac{493}{3} = 164.33 \text{ cm}^3$$ **Bottom-left: Purple pyramid** - $h = 4$, $G = 50$ cm$^2$ - Volume: $$V = \frac{1}{3} \times 50 \times 4 = \frac{200}{3} = 66.67 \text{ cm}^3$$ **Bottom-center: Magenta prism-like solid** - $h = 8$, $G = 36.5$ cm$^2$ - Volume: $$V = 36.5 \times 8 = 292 \text{ cm}^3$$ **Bottom-right: Orange prism** - $h = 22$, $G = 25$ cm$^2$ - Volume: $$V = 25 \times 22 = 550 \text{ cm}^3$$