Step-by-step explanation:
The diagram depicts a Right-Pyramid with a square base. The height of the pyramid is given as [tex]\dfrac{x}{2}\text{ in}[/tex] and the side of the base is given as [tex]x\text{ in}[/tex].
For any pyramid, the volume is given by the result
[tex]\text{Volume = }\dfrac{1}{3}\times \text{ Area of base }\times \text{ Height}[/tex]
So, Volume of given pyramid = [tex]\dfrac{1}{3}\times (x^{2}\text{ in}^{2}) \times(\dfrac{x}{2} \text{ in})=\dfrac{x^{3}}{6}\text{ in}^{3}[/tex]
Volume is given as [tex]288\text{ in}^{3}[/tex]
[tex]\dfrac{x^{3}}{6}\text{ = }288\text{ in}^{3}\\\\x^{3}\text{ = }1728\text{ in}^{3}\\x\text{ = }12\text{ in}[/tex]
∴ Value of [tex]x[/tex] = [tex]12\text{ in}[/tex]
Answer:
[tex]x=12in[/tex]
Step-by-step explanation:
the formula for the volume of a square pyramid is:
[tex]V=\frac{Ab*h}{3}[/tex]
where
[tex]Ab[/tex] is the area of the base (the area of the square)
and [tex]h[/tex] if the height of the pyramid
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the length of the side of the square is [tex]x[/tex], so the area of the base of the pyramid is:
[tex]Ab=x*x=x^2[/tex]
and we already know the height in terms of x:
[tex]h=\frac{1}{2}x[/tex]
and the Volume:
[tex]V=288in^3[/tex]
so we subtitute all of this in the formula for volume:
[tex]288=\frac{x^2(\frac{1}{2}x )}{3} \\288=\frac{x^3}{6}[/tex]
and finally we clear for [tex]x[/tex]
[tex]288*6=x^3\\1728=x^3\\\sqrt[3]{1728}=x\\12=x[/tex]
the value of x is 12 inches.
