benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Elliott Farms has a silo for storage. The silo is a right circular cylinder…

Problem

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

problem

Elliott Farms has a silo for storage. The silo is a right circular cylinder topped by a right circular cone, both having the same radius. The height of the cone is half the height of the cylinder. The diameter of the base of the silo is 10 meters and the height of the entire silo is 27 meters. What is the volume, in cubic meters, of the silo? Express your answer in terms of π\pi. [asy] size(150); draw((0,0)--(0,18)--(5,27)--(10,18)--(10,0),linewidth(1)); draw((0,0)..(5,-1)..(10,0),linewidth(1)); draw((0,0)..(5,1)..(10,0),linetype("0 4")+linewidth(1)); draw((0,18)..(5,17)..(10,18),linewidth(1)); draw((0,18)..(5,19)..(10,18),linetype("0 4")+linewidth(1)); draw((15,27)--(16,27),linewidth(1)); draw((15,0)--(16,0),linewidth(1)); draw((15.5,27)--(15.5,16),linewidth(1)); draw((15.5,0)--(15.5,11),linewidth(1)); label("27 meters",(15.5,13.5)); [/asy]
Plain-text mathematical notation (without MathML)
Elliott Farms has a silo for storage. The silo is a right circular cylinder topped by a right circular cone, both having the same radius. The height of the cone is half the height of the cylinder. The diameter of the base of the silo is 10 meters and the height of the entire silo is 27 meters. What is the volume, in cubic meters, of the silo? Express your answer in terms of π.

[asy]
size(150);
draw((0,0)--(0,18)--(5,27)--(10,18)--(10,0),linewidth(1));
draw((0,0)..(5,-1)..(10,0),linewidth(1));
draw((0,0)..(5,1)..(10,0),linetype("0 4")+linewidth(1));
draw((0,18)..(5,17)..(10,18),linewidth(1));
draw((0,18)..(5,19)..(10,18),linetype("0 4")+linewidth(1));

draw((15,27)--(16,27),linewidth(1));
draw((15,0)--(16,0),linewidth(1));
draw((15.5,27)--(15.5,16),linewidth(1));
draw((15.5,0)--(15.5,11),linewidth(1));
label("27 meters",(15.5,13.5));

[/asy]
Original LaTeX notation
Elliott Farms has a silo for storage. The silo is a right circular cylinder topped by a right circular cone, both having the same radius. The height of the cone is half the height of the cylinder. The diameter of the base of the silo is 10 meters and the height of the entire silo is 27 meters. What is the volume, in cubic meters, of the silo? Express your answer in terms of $\pi$.

[asy]
size(150);
draw((0,0)--(0,18)--(5,27)--(10,18)--(10,0),linewidth(1));
draw((0,0)..(5,-1)..(10,0),linewidth(1));
draw((0,0)..(5,1)..(10,0),linetype("0 4")+linewidth(1));
draw((0,18)..(5,17)..(10,18),linewidth(1));
draw((0,18)..(5,19)..(10,18),linetype("0 4")+linewidth(1));

draw((15,27)--(16,27),linewidth(1));
draw((15,0)--(16,0),linewidth(1));
draw((15.5,27)--(15.5,16),linewidth(1));
draw((15.5,0)--(15.5,11),linewidth(1));
label("27 meters",(15.5,13.5));

[/asy]

level

Level 3

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
e04011cb-97e1-563a-89f7-f0c7e6d5cd9a
task_key
geometry--test--e04011cb-97e1-563a-89f7-f0c7e6d5cd9a
task_revision_id
1
config / split
geometry / test

Official source

initial import