Pyramidal 44061

A pyramidal candle with a square base has a side edge of s = 12 cm and a base edge of 4 cm. How much wax will we need to make it, and how long is the wick if it is 5% bigger than its height?

Final Answer:

V =  62.1968 cm³
x =  12.245 cm

Step-by-step explanation:

$$\begin{gathered} s=12\text{cm} \\ a=4\text{cm} \\ {S}_1=a^2=4^2=16{\text{cm}}^2 \\ u=\sqrt{2}\cdot a=\sqrt{2}\cdot 4=4\sqrt{2}\text{cm}\doteq 5.6569\text{cm} \\ h=\sqrt{s^2-(u/2{)}^2}=\sqrt{12^2-(5.6569/2{)}^2}=2\sqrt{34}\text{cm}\doteq 11.6619\text{cm} \\ V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 16\cdot 11.6619=62.1968{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} q=100\%+5\%=1+\frac{5}{100}=1.05 \\ x=q\cdot h=1.05\cdot 11.6619=12.245\text{cm} \end{gathered}$$

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