Sarhaw8231idn
Answered

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The volume of an oblique pyramid with a square base is [tex]V[/tex] units[tex]\(^3\)[/tex] and the height is [tex]h[/tex] units. Which expression represents the area of the base of the pyramid?

A. [tex]\frac{3V}{h}[/tex] units[tex]\(^2\)[/tex]

B. [tex]3V - h[/tex] units[tex]\(^2\)[/tex]

C. [tex]V - 3h[/tex] units[tex]\(^2\)[/tex]

Sagot :

GinnyAnsweridn
To find the area of the base of an oblique pyramid with a square base and given volume [tex]\( V \)[/tex] and height [tex]\( h \)[/tex], let's use the relationship between the volume, base area, and height of a pyramid.

The volume [tex]\( V \)[/tex] of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{BaseArea} \times h \][/tex]

Here, we need to solve for the BaseArea. We start by isolating BaseArea in the equation:
[tex]\[ V = \frac{1}{3} \times \text{BaseArea} \times h \][/tex]

First, multiply both sides by 3 to clear the fraction:
[tex]\[ 3V = \text{BaseArea} \times h \][/tex]

Next, divide both sides by [tex]\( h \)[/tex] to solve for \text{BaseArea}:
[tex]\[ \text{BaseArea} = \frac{3V}{h} \][/tex]

So, the expression that represents the area of the base of the pyramid is:
[tex]\[ \frac{3V}{h} \text{ units }^2 \][/tex]

Among the given options, the correct expression is:
[tex]\[ \boxed{\frac{3 V}{h} \text{ units }^{2}} \][/tex]
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