IDNLearn.com: Your reliable source for finding expert answers. Explore a wide array of topics and find reliable answers from our experienced community members.
Sagot :
To determine the height of a solid right pyramid with a square base, we need to start with the formula for its volume. The volume [tex]\( V \)[/tex] of a pyramid can be expressed as:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
In this case, the base of the pyramid is a square with edge length [tex]\( y \)[/tex]. Therefore, the area of the square base is:
[tex]\[ \text{Base Area} = y^2 \][/tex]
Substituting the base area into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times y^2 \times \text{Height} \][/tex]
Let [tex]\( h \)[/tex] represent the height of the pyramid. The equation then becomes:
[tex]\[ V = \frac{1}{3} \times y^2 \times h \][/tex]
We want to solve for the height [tex]\( h \)[/tex]. To do this, we rearrange the equation to isolate [tex]\( h \)[/tex]:
[tex]\[ h = \frac{3 \times V}{y^2} \][/tex]
Thus, the correct expression for the height of the pyramid is:
[tex]\[ \frac{3V}{y^2} \text{ units} \][/tex]
Among the given options:
1. [tex]\(\frac{3 V}{y^2}\)[/tex] units
2. [tex]\((3 V - y^2)\)[/tex] units
3. [tex]\((V - 3 y^2)\)[/tex] units
4. [tex]\(\frac{V}{3 y^2}\)[/tex] units
The correct expression that represents the height of the pyramid is:
[tex]\[ \frac{3 V}{y^2} \text{ units} \][/tex]
So, the correct choice is:
[tex]\[ \boxed{\frac{3 V}{y^2}} \text{ units} \][/tex]
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
In this case, the base of the pyramid is a square with edge length [tex]\( y \)[/tex]. Therefore, the area of the square base is:
[tex]\[ \text{Base Area} = y^2 \][/tex]
Substituting the base area into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times y^2 \times \text{Height} \][/tex]
Let [tex]\( h \)[/tex] represent the height of the pyramid. The equation then becomes:
[tex]\[ V = \frac{1}{3} \times y^2 \times h \][/tex]
We want to solve for the height [tex]\( h \)[/tex]. To do this, we rearrange the equation to isolate [tex]\( h \)[/tex]:
[tex]\[ h = \frac{3 \times V}{y^2} \][/tex]
Thus, the correct expression for the height of the pyramid is:
[tex]\[ \frac{3V}{y^2} \text{ units} \][/tex]
Among the given options:
1. [tex]\(\frac{3 V}{y^2}\)[/tex] units
2. [tex]\((3 V - y^2)\)[/tex] units
3. [tex]\((V - 3 y^2)\)[/tex] units
4. [tex]\(\frac{V}{3 y^2}\)[/tex] units
The correct expression that represents the height of the pyramid is:
[tex]\[ \frac{3 V}{y^2} \text{ units} \][/tex]
So, the correct choice is:
[tex]\[ \boxed{\frac{3 V}{y^2}} \text{ units} \][/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.