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MATH / A belt is drawn tightly around three circles of radius 10 cm each, as shown. The length of the belt, in cm, can be written in the form a+bπ for rational numbers a and b. What is th…

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problem

A belt is drawn tightly around three circles of radius 1010 cm each, as shown. The length of the belt, in cm, can be written in the form a+bπa + b\pi for rational numbers aa and bb. What is the value of a+ba + b? [asy] size(120); defaultpen(linewidth(0.8)); picture p; real r = 3^.5/2; pair A = expi(-pi/6); draw(p, circle(A, r)); draw(p, (A.x,A.y - r) -- (-A.x,A.y - r)); add(p); add(rotate(120)*p); add(rotate(240)*p); [/asy]
Plain-text mathematical notation (without MathML)
A belt is drawn tightly around three circles of radius 10 cm each, as shown. The length of the belt, in cm, can be written in the form a+bπ for rational numbers a and b. What is the value of a+b? [asy]

size(120); defaultpen(linewidth(0.8));
picture p; real r = 3^.5/2;
pair A = expi(-pi/6); draw(p, circle(A, r)); draw(p, (A.x,A.y - r) -- (-A.x,A.y - r));
add(p); add(rotate(120)*p); add(rotate(240)*p);
[/asy]
Original LaTeX notation
A belt is drawn tightly around three circles of radius $10$ cm each, as shown. The length of the belt, in cm, can be written in the form $a + b\pi$ for rational numbers $a$ and $b$. What is the value of $a + b$? [asy]

size(120); defaultpen(linewidth(0.8));
picture p; real r = 3^.5/2;
pair A = expi(-pi/6); draw(p, circle(A, r)); draw(p, (A.x,A.y - r) -- (-A.x,A.y - r));
add(p); add(rotate(120)*p); add(rotate(240)*p);
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
9c78ec89-cc27-5d43-a11c-4a9aee206275
task_key
geometry--test--9c78ec89-cc27-5d43-a11c-4a9aee206275
task_revision_id
1
config / split
geometry / test

Official source

initial import