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MATH / What is the volume of a pyramid whose base is one face of a cube of side length…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

What is the volume of a pyramid whose base is one face of a cube of side length 22, and whose apex is the center of the cube? Give your answer in simplest form. [asy] import three; triple A,B,C,D,EE,F,G,H; A = (0,0,0); B = (1,0,0); C = (1,1,0); D= (0,1,0); EE = (0,0,1); F = B+EE; G = C + EE; H = D + EE; O = G/2; draw(surface(B--O--C--cycle),red,nolight); draw(surface(C--O--D--cycle),red+white,nolight); draw(B--C--D); draw(B--A--D,dashed); draw(EE--F--G--H--EE); draw(A--EE,dashed); draw(B--F); draw(C--G); draw(D--H); draw(A--O--C,dashed); draw(B--O--D,dashed); dot(A); dot(B); dot(C); dot(D); dot(EE); dot(F); dot(G); dot(H); dot(O); [/asy]
Plain-text mathematical notation (without MathML)
What is the volume of a pyramid whose base is one face of a cube of side length 2, and whose apex is the center of the cube? Give your answer in simplest form.

[asy]
import three;
triple A,B,C,D,EE,F,G,H;
A = (0,0,0);
B = (1,0,0);
C = (1,1,0);
D= (0,1,0);
EE = (0,0,1);
F = B+EE;
G = C + EE;
H = D + EE;
O = G/2;
draw(surface(B--O--C--cycle),red,nolight);
draw(surface(C--O--D--cycle),red+white,nolight);
draw(B--C--D);
draw(B--A--D,dashed);
draw(EE--F--G--H--EE);
draw(A--EE,dashed);
draw(B--F);
draw(C--G);
draw(D--H);
draw(A--O--C,dashed);
draw(B--O--D,dashed);
dot(A); dot(B); dot(C); dot(D); dot(EE); dot(F); dot(G); dot(H); dot(O);
[/asy]
Original LaTeX notation
What is the volume of a pyramid whose base is one face of a cube of side length $2$, and whose apex is the center of the cube? Give your answer in simplest form.

[asy]
import three;
triple A,B,C,D,EE,F,G,H;
A = (0,0,0);
B = (1,0,0);
C = (1,1,0);
D= (0,1,0);
EE = (0,0,1);
F = B+EE;
G = C + EE;
H = D + EE;
O = G/2;
draw(surface(B--O--C--cycle),red,nolight);
draw(surface(C--O--D--cycle),red+white,nolight);
draw(B--C--D);
draw(B--A--D,dashed);
draw(EE--F--G--H--EE);
draw(A--EE,dashed);
draw(B--F);
draw(C--G);
draw(D--H);
draw(A--O--C,dashed);
draw(B--O--D,dashed);
dot(A); dot(B); dot(C); dot(D); dot(EE); dot(F); dot(G); dot(H); dot(O);
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
db58e55e-d474-58c6-becb-0173d46717aa
task_key
geometry--test--db58e55e-d474-58c6-becb-0173d46717aa
task_revision_id
1
config / split
geometry / test

Official source

initial import