The soap

The soap has the shape of a cuboid with dimensions of 6 cm, 4 cm, and 2 cm. Katy used it for a week and all the dimensions of the soap shrunk by half. How long will her soap last?

Final Answer:

t =  1 d

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ b=4\text{cm} \\ c=2\text{cm} \\ x=a/2=6/2=3\text{cm} \\ y=b/2=4/2=2\text{cm} \\ z=c/2=2/2=1\text{cm} \\ {V}_1=a\cdot b\cdot c=6\cdot 4\cdot 2=48{\text{cm}}^3 \\ {V}_2=x\cdot y\cdot z=3\cdot 2\cdot 1=6{\text{cm}}^3 \\ {V}_1-V_2\dots 7days \\ {V}_2\dots .t \\ t/7=V_2/(V_1-V_2) \\ t=7\cdot V_2/(V_1-V_2)=7\cdot 6/(48-6)=1\text{d} \end{gathered}$$

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