Body surfaces

The cuboid's volume is 864 mm³. Its square base has the same area as the base of a quadrilateral prism, with dimensions 7 cm and 9 cm, the height of the base 4 cm, and the height of the prism 15 cm. Find the surfaces of both bodies.

Final Answer:

S₁ =  126.4354 cm²
S₂ =  606 cm²

Step-by-step explanation:

$$\begin{gathered} a=7\text{cm} \\ b=9\text{cm} \\ c=15\text{cm} \\ S=a\cdot b=7\cdot 9=63{\text{cm}}^2 \\ {V}_1=864{\text{mm}}^3\to {\text{cm}}^3=864:1000{\text{cm}}^3=0.864{\text{cm}}^3 \\ {c}_1=V_1/S=0.864/63=\frac{12}{875}\doteq 0.0137\text{cm} \\ {a}_1=\sqrt{S}=\sqrt{63}=3\sqrt{7}\text{cm}\doteq 7.9373\text{cm} \\ {S}_1=2\cdot S+4\cdot a_1\cdot c_1=2\cdot 63+4\cdot 7.9373\cdot 0.0137=126.4354{\text{cm}}^2 \end{gathered}$$

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

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