Quadrilateral 8060

The volume of the cuboid is 864 mm³. Its square shape has the same content as the base of a quadrilateral prism with the dimensions of the base 7cm and 9cm, the height of the base 4cm, and the height of the prism 15cm. Determine the surface areas of both bodies.

Correct answer:

S₁ =  0.4354 cm²
S₂ =  606 cm²

Step-by-step explanation:

$$\begin{gathered} a=7\text{cm} \\ b=9\text{cm} \\ c=15\text{cm} \\ S=a\cdot b=7\cdot 9=63{\text{cm}}^2 \\ {V}_1=864{\text{mm}}^3\to {\text{cm}}^3=864:1000{\text{cm}}^3=0.864{\text{cm}}^3 \\ {c}_1=V_1/S=0.864/63=\frac{12}{875}\doteq 0.0137\text{cm} \\ {a}_1=\sqrt{S}=\sqrt{63}=3\sqrt{7}\text{cm}\doteq 7.9373\text{cm} \\ {S}_1=2\cdot S_2+4\cdot a_1\cdot c_1=2\cdot S_2+4\cdot 7.9373\cdot 0.0137=0.4354{\text{cm}}^2 \end{gathered}$$

$S_2=2\cdot (a\cdot b+b\cdot c+a\cdot c)=2\cdot (7\cdot 9+9\cdot 15+7\cdot 15)=606{\text{cm}}^2$

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