Calculate 64584

The base of the block is a square with an area of 16 cm². The surface of the block is 128 cm². You calculate the volume of the block in cm³.

Correct answer:

V =  96 cm³

Step-by-step explanation:

$$\begin{gathered} S_1=16{\text{cm}}^2 \\ S=128{\text{cm}}^2 \\ {S}_1=a^2 \\ a=\sqrt{S_1}=\sqrt{16}=4\text{cm} \\ S=2\cdot S_1+4\cdot a\cdot c \\ c=\frac{S-2\cdot S_1}{4\cdot a}=\frac{128-2\cdot 16}{4\cdot 4}=6\text{cm} \\ V=S_1\cdot c=16\cdot 6=96{\text{cm}}^3 \end{gathered}$$

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