A cuboid 2

A cuboid with a depth of 4 cm but a length and width of x cm is cut out from one corner of the original cuboid as shown (the original cuboid has dimensions of 10x8x4 cm). The remaining shape has a volume of 199 cm³. Calculate the value of x.

Correct answer:

x =  5.5 cm

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ b=8\text{cm} \\ c=4\text{cm} \\ {V}_1=a\cdot b\cdot c=10\cdot 8\cdot 4=320{\text{cm}}^3 \\ {V}_2=199{\text{cm}}^3 \\ {V}_1-x\cdot x\cdot c=V_2 \\ x\cdot x\cdot c=V_1-V_2 \\ x=\sqrt{\frac{V_1-V_2}{c}}=\sqrt{\frac{320-199}{4}}=5.5\text{cm} \end{gathered}$$

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