Flowerpot

The block-shaped flowerpot has external dimensions: length 1.25 m, width 10 cm and height 11 cm. The thickness of the boards from which it is made is 0.8 cm. How many liters of soil is needed to fill it 1 cm below the top edge? What surface do we have to paint if we only paint the outer surface of the flowerpot?

Correct answer:

V =  10.4693 l
S =  42.2 dm²

Step-by-step explanation:

$$\begin{gathered} a=1.25\text{ m}\to \text{ dm}=1.25\cdot 10\text{ dm}=12.5\text{ dm } \\ b=10\text{ cm}\to \text{ dm}=10\mathrm{/}10\text{ dm}=1\text{ dm } \\ c=11\text{ cm}\to \text{ dm}=11\mathrm{/}10\text{ dm}=1.1\text{ dm } \\ h=0.8\text{ cm}\to \text{ dm}=0.8\mathrm{/}10\text{ dm}=0.08\text{ dm } \\ {h}_1=1\text{ cm}\to \text{ m}=1\mathrm{/}100\text{ m}=0.01\text{ m } \\ {a}_1=a-2\cdot h=12.5-2\cdot 0.08={\displaystyle \frac{617}{50}}=12.34\text{ dm } \\ {b}_1=b-2\cdot h=1-2\cdot 0.08={\displaystyle \frac{21}{25}}=0.84\text{ dm } \\ {c}_1=c-h-h_1=1.1-0.08-0.01={\displaystyle \frac{101}{100}}=1.01\text{ dm } \\ V=a_1\cdot b_1\cdot c_1=12.34\cdot 0.84\cdot 1.01=10.4693\text{ l} \end{gathered}$$

$S=a\cdot b+2\cdot b\cdot c+2\cdot c\cdot a=12.5\cdot 1+2\cdot 1\cdot 1.1+2\cdot 1.1\cdot 12.5={\displaystyle \frac{211}{5}}={\displaystyle \frac{211}{5}}{\text{dm}}^2=42.2{\text{dm}}^2$

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