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Plane cutting a pyramid
The Next CEO of Stack OverflowRight Pyramid questionA pyramid has a square base with sides of length 4. If the sides of the pyramid are equilateral triangles, what is the pyramid's volume?Volume of pentahedron having all sides of length 1?What is the ratio of the volume of the pyramid to the volume of the cube?Relation between slant edge and height of a pyramid with an equlateral triangle as its baseVolume of a pyramid with equilateral triangle as baseA sphere circumscribing a truncated rectangular pyramidHow can I find an expression for the area of cross sections of the given solid as a function of $x$?Compute the dihedral angle of a regular pyramidFind the volume of the pyramid
$begingroup$
Pyramid with equilateral triangle as a base, length of side of pyramid is $s=3$(not a base side). Plane goes through pyramid, and contains base edge, and is normal to a side of pyramid. If surface area of that cutting through with plane through pyramid is $14$, what is the volume of the pyramid.
My attempt at solution: I know that figure formed by cutting through with plane is a isosceles triangle, and I tried to connect height of that pyramid with a side of the pyramid. But having trouble to find connection, can't really represent it with formula.
geometry
asked Mar 20 at 11:18
Darko DekanDarko Dekan
331213
$endgroup$
add a comment |
$begingroup$
Pyramid with equilateral triangle as a base, length of side of pyramid is $s=3$(not a base side). Plane goes through pyramid, and contains base edge, and is normal to a side of pyramid. If surface area of that cutting through with plane through pyramid is $14$, what is the volume of the pyramid.
My attempt at solution: I know that figure formed by cutting through with plane is a isosceles triangle, and I tried to connect height of that pyramid with a side of the pyramid. But having trouble to find connection, can't really represent it with formula.
geometry
asked Mar 20 at 11:18
Darko DekanDarko Dekan
331213
$endgroup$
add a comment |
$begingroup$
Pyramid with equilateral triangle as a base, length of side of pyramid is $s=3$(not a base side). Plane goes through pyramid, and contains base edge, and is normal to a side of pyramid. If surface area of that cutting through with plane through pyramid is $14$, what is the volume of the pyramid.
My attempt at solution: I know that figure formed by cutting through with plane is a isosceles triangle, and I tried to connect height of that pyramid with a side of the pyramid. But having trouble to find connection, can't really represent it with formula.
geometry
asked Mar 20 at 11:18
Darko DekanDarko Dekan
331213
$endgroup$
Pyramid with equilateral triangle as a base, length of side of pyramid is $s=3$(not a base side). Plane goes through pyramid, and contains base edge, and is normal to a side of pyramid. If surface area of that cutting through with plane through pyramid is $14$, what is the volume of the pyramid.
My attempt at solution: I know that figure formed by cutting through with plane is a isosceles triangle, and I tried to connect height of that pyramid with a side of the pyramid. But having trouble to find connection, can't really represent it with formula.
geometry
geometry
asked Mar 20 at 11:18
Darko DekanDarko Dekan
331213
asked Mar 20 at 11:18
Darko DekanDarko Dekan
331213
asked Mar 20 at 11:18
Darko DekanDarko Dekan
331213
asked Mar 20 at 11:18
Darko DekanDarko Dekan
331213
asked Mar 20 at 11:18
Darko DekanDarko Dekan
331213
331213
add a comment |
add a comment |
1 Answer
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Note that by that plane, the pyramid is cut into two tetrahedrons with base area 14 and sum of their heights equal to $s=3$. Since the volume of tetrahedron is given by $displaystyle V=frac Sh 3$ where $S$ is a base area and $h$ is a height from the base to apex, the volume of the pyramid is
$$
frac14(h_1+h_2)3=frac14times 33=14.
$$
answered Mar 20 at 11:26
SongSong
18.5k21651
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$begingroup$
Note that by that plane, the pyramid is cut into two tetrahedrons with base area 14 and sum of their heights equal to $s=3$. Since the volume of tetrahedron is given by $displaystyle V=frac Sh 3$ where $S$ is a base area and $h$ is a height from the base to apex, the volume of the pyramid is
$$
frac14(h_1+h_2)3=frac14times 33=14.
$$
answered Mar 20 at 11:26
SongSong
18.5k21651
$endgroup$
add a comment |
$begingroup$
Note that by that plane, the pyramid is cut into two tetrahedrons with base area 14 and sum of their heights equal to $s=3$. Since the volume of tetrahedron is given by $displaystyle V=frac Sh 3$ where $S$ is a base area and $h$ is a height from the base to apex, the volume of the pyramid is
$$
frac14(h_1+h_2)3=frac14times 33=14.
$$
answered Mar 20 at 11:26
SongSong
18.5k21651
$endgroup$
add a comment |
$begingroup$
Note that by that plane, the pyramid is cut into two tetrahedrons with base area 14 and sum of their heights equal to $s=3$. Since the volume of tetrahedron is given by $displaystyle V=frac Sh 3$ where $S$ is a base area and $h$ is a height from the base to apex, the volume of the pyramid is
$$
frac14(h_1+h_2)3=frac14times 33=14.
$$
answered Mar 20 at 11:26
SongSong
18.5k21651
$endgroup$
Note that by that plane, the pyramid is cut into two tetrahedrons with base area 14 and sum of their heights equal to $s=3$. Since the volume of tetrahedron is given by $displaystyle V=frac Sh 3$ where $S$ is a base area and $h$ is a height from the base to apex, the volume of the pyramid is
$$
frac14(h_1+h_2)3=frac14times 33=14.
$$
answered Mar 20 at 11:26
SongSong
18.5k21651
answered Mar 20 at 11:26
SongSong
18.5k21651
answered Mar 20 at 11:26
SongSong
18.5k21651
answered Mar 20 at 11:26
SongSong
18.5k21651
18.5k21651
add a comment |
add a comment |
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