Subjects geometry

Chocolate Filling 9Cca21

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1. **Problem statement:** Calculate the capacity of the chocolate filling inside the solid, which consists of a rectangular prism with a triangular prism on top. 2. **Understanding the shape:** The solid is composed of two parts: - A rectangular prism (box) at the bottom. - A triangular prism on top. 3. **Formula for volume:** - Volume of rectangular prism = $\text{length} \times \text{width} \times \text{height}$ - Volume of triangular prism = $\frac{1}{2} \times \text{base} \times \text{height of triangle} \times \text{length}$ 4. **Calculate volumes:** - Let the dimensions of the rectangular prism be $l$, $w$, and $h_1$. - Let the triangular prism have base $b$, height $h_2$, and length $l$ (same as rectangular prism length). 5. **Total volume of solid:** $$V_{total} = l \times w \times h_1 + \frac{1}{2} \times b \times h_2 \times l$$ 6. **Capacity of chocolate filling:** - The filling is inside the solid, so its volume equals the total volume calculated. - Convert volume from cubic centimeters to liters by dividing by 1000. 7. **Example calculation:** - Suppose $l=10$ cm, $w=5$ cm, $h_1=4$ cm, $b=5$ cm, $h_2=3$ cm. Calculate rectangular prism volume: $$V_{rect} = 10 \times 5 \times 4 = 200 \text{ cm}^3$$ Calculate triangular prism volume: $$V_{tri} = \frac{1}{2} \times 5 \times 3 \times 10 = 75 \text{ cm}^3$$ Total volume: $$V_{total} = 200 + 75 = 275 \text{ cm}^3$$ Convert to liters: $$\text{Capacity} = \frac{275}{1000} = 0.275 \text{ liters}$$ 8. **Final answer:** The capacity of the chocolate filling is $\boxed{0.28}$ liters (rounded to 2 decimal places).