benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / A cube of edge length s>0 has the property that its surface area is equal to the sum of its volume and five times its edge length. Compute the sum of all possible values of s. [asy…

Problem

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

problem

A cube of edge length s>0s > 0 has the property that its surface area is equal to the sum of its volume and five times its edge length. Compute the sum of all possible values of ss. [asy] size(5cm,5cm); pair A,B,C,D,E,F,G,H; A=(0,0); B=(1,0); C=(1,1); D=(0,1); E=(0.3,1.5); F=C+(E-D); G=B+(E-D); H=A+(E-D); draw(A--B--C--D--A--H--E); draw(D--C--F); draw(H--G); draw(D--E--F--G--B); dot(A); dot(B); dot(C); dot(D); dot(E); dot(F); dot(G); dot(H); [/asy]
Plain-text mathematical notation (without MathML)
A cube of edge length s>0 has the property that its surface area is equal to the sum of its volume and five times its edge length. Compute the sum of all possible values of s.

[asy]

size(5cm,5cm);

pair A,B,C,D,E,F,G,H;

A=(0,0);
B=(1,0);
C=(1,1);
D=(0,1);
E=(0.3,1.5);
F=C+(E-D);
G=B+(E-D);
H=A+(E-D);

draw(A--B--C--D--A--H--E);
draw(D--C--F);
draw(H--G);
draw(D--E--F--G--B);

dot(A);
dot(B);
dot(C);
dot(D);
dot(E);
dot(F);
dot(G);
dot(H);

[/asy]
Original LaTeX notation
A cube of edge length $s > 0$ has the property that its surface area is equal to the sum of its volume and five times its edge length. Compute the sum of all possible values of $s$.

[asy]

size(5cm,5cm);

pair A,B,C,D,E,F,G,H;

A=(0,0);
B=(1,0);
C=(1,1);
D=(0,1);
E=(0.3,1.5);
F=C+(E-D);
G=B+(E-D);
H=A+(E-D);

draw(A--B--C--D--A--H--E);
draw(D--C--F);
draw(H--G);
draw(D--E--F--G--B);

dot(A);
dot(B);
dot(C);
dot(D);
dot(E);
dot(F);
dot(G);
dot(H);

[/asy]

level

Level 4

type

Geometry

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
5c915f2f-cbae-502e-9d1e-f0f28d2bcab5
task_key
geometry--test--5c915f2f-cbae-502e-9d1e-f0f28d2bcab5
task_revision_id
1
config / split
geometry / test

Official source

initial import