Percentage 66684

Prism with square base a=25cm, height h=45cm. cube: b=15cm
a) what percentage of the volume of the prism is the volume of the cube?
b) what height should the prism have to have the same volume as the cube?

Correct answer:

p =  12 %
h₂ =  5.4 cm

Step-by-step explanation:

$$\begin{gathered} a=25\text{cm} \\ h=45\text{cm} \\ b=15\text{cm} \\ {V}_1=a\cdot a\cdot h=25\cdot 25\cdot 45=28125{\text{cm}}^3 \\ {V}_2=b^3=15^3=3375{\text{cm}}^3 \\ p=100\cdot \frac{V_2}{V_1}=100\cdot \frac{3375}{28125}=\frac{100\cdot 3375}{28125}=\frac{337500}{28125}=12\% \end{gathered}$$

$$\begin{gathered} V_3=V_2 \\ {a}^2\cdot h_2=V_2 \\ {h}_2=\frac{V_2}{a^2}=\frac{3375}{25^2}=\frac{27}{5}\text{cm}=5.4\text{cm} \end{gathered}$$

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