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MATH / Assume that the length of Earth's equator is exactly 25,100 miles and that the…

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

problem

Assume that the length of Earth's equator is exactly 25,100 miles and that the Earth is a perfect sphere. The town of Lena, Wisconsin, is at 45∘45^{\circ} North Latitude, exactly halfway between the equator and the North Pole. What is the number of miles in the circumference of the circle on Earth parallel to the equator and through Lena, Wisconsin? Express your answer to the nearest hundred miles. (You may use a calculator for this problem.) [asy] size(4.5cm,4.5cm); draw(unitcircle); draw((-1,0)..(0,-0.2)..(1,0)); draw((-0.95,0.05)..(0,0.2)..(0.97,0.05),1pt+dotted); draw((-0.7,0.7)..(0,0.6)..(0.7,0.7)); draw((-0.65,0.75)..(0,0.8)..(0.66,0.75),1pt+dotted); dot((0,0)); draw((0,0)--(1,0)); draw((0,0)--(0.7,0.7)); dot((0.7,0.7)); dot((0,0.72)); label("Lena",(0.7,0.7),ENE); label("45∘45^\circ",shift(0.3,0.1)*(0,0)); [/asy]
Plain-text mathematical notation (without MathML)
Assume that the length of Earth's equator is exactly 25,100 miles and that the Earth is a perfect sphere. The town of Lena, Wisconsin, is at 45^(∘) North Latitude, exactly halfway between the equator and the North Pole. What is the number of miles in the circumference of the circle on Earth parallel to the equator and through Lena, Wisconsin? Express your answer to the nearest hundred miles.  (You may use a calculator for this problem.)

[asy]
size(4.5cm,4.5cm);
draw(unitcircle);
draw((-1,0)..(0,-0.2)..(1,0));
draw((-0.95,0.05)..(0,0.2)..(0.97,0.05),1pt+dotted);
draw((-0.7,0.7)..(0,0.6)..(0.7,0.7));
draw((-0.65,0.75)..(0,0.8)..(0.66,0.75),1pt+dotted);
dot((0,0));
draw((0,0)--(1,0));
draw((0,0)--(0.7,0.7));
dot((0.7,0.7));
dot((0,0.72));
label("Lena",(0.7,0.7),ENE);
label("45^(∘)",shift(0.3,0.1)*(0,0));
[/asy]
Original LaTeX notation
Assume that the length of Earth's equator is exactly 25,100 miles and that the Earth is a perfect sphere. The town of Lena, Wisconsin, is at $45^{\circ}$ North Latitude, exactly halfway between the equator and the North Pole. What is the number of miles in the circumference of the circle on Earth parallel to the equator and through Lena, Wisconsin? Express your answer to the nearest hundred miles.  (You may use a calculator for this problem.)

[asy]
size(4.5cm,4.5cm);
draw(unitcircle);
draw((-1,0)..(0,-0.2)..(1,0));
draw((-0.95,0.05)..(0,0.2)..(0.97,0.05),1pt+dotted);
draw((-0.7,0.7)..(0,0.6)..(0.7,0.7));
draw((-0.65,0.75)..(0,0.8)..(0.66,0.75),1pt+dotted);
dot((0,0));
draw((0,0)--(1,0));
draw((0,0)--(0.7,0.7));
dot((0.7,0.7));
dot((0,0.72));
label("Lena",(0.7,0.7),ENE);
label("$45^\circ$",shift(0.3,0.1)*(0,0));
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
827f0805-2519-5f3d-86ac-43c3b0a507bc
task_key
geometry--test--827f0805-2519-5f3d-86ac-43c3b0a507bc
task_revision_id
1
config / split
geometry / test

Official source

initial import