Mr. Gardener

Mr. Gardener wants to make wood for the balcony. Boxes. Each will have the shape of a perpendicular prism with a square base. The height is limited to 60 cm. He will fill each container with soil by pouring the whole bag of substrate sold into a package containing 80 l. The soil reaches 10 cm from the upper edge of the container. How long will the inner edge of such a box be?

Correct answer:

a =  40 cm

Step-by-step explanation:

$$\begin{gathered} c=60\text{cm} \\ {c}_2=10\text{cm} \\ {V}_2=80\text{l}\to {\text{cm}}^3=80\cdot 1000{\text{cm}}^3=80000{\text{cm}}^3 \\ {V}_2=a^2\cdot (c-c_2) \\ a=\sqrt{\frac{V_2}{c-c_2}}=\sqrt{\frac{80000}{60-10}}=40\text{cm} \end{gathered}$$

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