Trapezoidal 24731

Calculate how many candies fit in a box shaped like a 4-sided prism with a trapezoidal base with base dimensions of 20 cm and 3.2 cm. The distance between the bases is 50 mm. The container is 32 cm high, and 1 candy occupies 2.5 cm³ of volume.

Correct answer:

n =  742

Step-by-step explanation:

$$\begin{gathered} a=20\text{cm} \\ c=3.2\text{cm} \\ v=50\text{mm}\to \text{cm}=50:10\text{cm}=5\text{cm} \\ h=32\text{cm} \\ {V}_1=2.5{\text{cm}}^3 \\ {S}_1=\frac{a+c}{2}\cdot v=\frac{20+3.2}{2}\cdot 5=58{\text{cm}}^2 \\ V=S_1\cdot h=58\cdot 32=1856{\text{cm}}^3 \\ n=\lfloor V/V_1\rfloor =\lfloor 1856/2.5\rfloor =742 \end{gathered}$$

Try another example