Answered

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The volume of a solid right pyramid with a square base is [tex]V[/tex] units[tex]\(^3\)[/tex] and the length of the base edge is [tex]y[/tex] units.

Which expression represents the height of the pyramid?

A. [tex]\frac{3V}{y^2}[/tex] units
B. [tex]3V - y^2[/tex] units
C. [tex]V - 3y^2[/tex] units
D. [tex]\frac{V}{3y^2}[/tex] units

Sagot :

GinnyAnswer
To find the height of a solid right pyramid with a square base, we start with the formula for the volume of the pyramid:

[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]

Given that the base is a square with edge length [tex]\( y \)[/tex], the base area can be written as:

[tex]\[ \text{base area} = y^2 \][/tex]

Now, substituting the base area into the volume formula, we get:

[tex]\[ V = \frac{1}{3} \times y^2 \times \text{height} \][/tex]

Rearranging this formula to solve for the height, we have:

[tex]\[ 3V = y^2 \times \text{height} \][/tex]

Now, isolating the height on one side of the equation:

[tex]\[ \text{height} = \frac{3V}{y^2} \][/tex]

Hence, the expression that represents the height of the pyramid is:

[tex]\[ \frac{3V}{y^2} \][/tex]

So, the correct option is:

[tex]\[ \frac{3V}{y^2} \][/tex] units
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