50 free Archimedes trivia questions with answers — science & nature quiz, new questions added Aug 2026.
Archimedes of Syracuse worked out the law of buoyancy, the law of the lever, a value of pi accurate to two decimal places and the volume of a sphere, then invented a number system to count the grains of sand it would take to fill the universe. He also built the catapults and cranes that held off a Roman army, and was killed by a soldier while drawing in the dust. This quiz covers the mathematics, the machines, the legends and the astonishing afterlife of his lost manuscripts. Easy questions ask what he supposedly shouted in the bath, what his screw did and where he lived. Harder ones want the king whose wreath he tested, the two bounds he found for pi, the shape carved on his tomb, the number in the Sand Reckoner, the name of his 14-piece puzzle, the treatise that survived only under a book of prayers, the auction price of that Palimpsest, the ship named for his screw and the US state whose motto is his exclamation. Every answer was checked against Wikipedia's article on Archimedes, and each question carries the sentence that supports it. Made for maths and physics teachers, students and quiz hosts. Related quizzes: Ancient Greece, Famous Mathematicians and Physics.
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Q 01On which island was Archimedes' home city, where he was born and killed?
Sicily
The city was a self-governing Greek colony in Magna Graecia when he was born around 287 BC.
Q 02What did Archimedes supposedly cry as he ran naked through the streets after his bathtub insight?
Eureka!
The word means "I have found it!" and is now the state motto of California, referring to the 1848 gold discovery.
Q 03Which king of Syracuse asked Archimedes to check whether his gold wreath was cut with silver?
Hiero II
According to Vitruvius the wreath displaced more water than pure gold and less than silver, proving the goldsmith a cheat.
Q 04Which Roman writer, two centuries after Archimedes died, is the source of the bathtub story?
Vitruvius
A rival 5th-century poem, Carmen de Ponderibus, has him use a balance dipped in water instead.
Q 05Archimedes' principle states that a body immersed in water experiences an upthrust equal to what?
The weight of fluid it displaces
It appears in his treatise On Floating Bodies, which survives in Greek only in the Palimpsest.
Q 06Which oft-quoted remark about leverage does Pappus of Alexandria attribute to Archimedes?
"Give me a place to stand on, and I will move the Earth."
It arose from a boast to King Hiero that he could move any weight, which the king answered by challenging him to move a ship.
Q 07What was the Syracusia, which Archimedes is said to have launched?
The largest ship built in classical antiquity
Plutarch says he moved it with a block-and-tackle pulley system; Hero of Alexandria credits a windlass called the baroulkos.
Q 08What is the modern verdict on whether Archimedes invented the water-lifting screw named after him?
It likely predates him by a significant amount
None of the contemporaries who describe its use, including Vitruvius and Strabo, credit him with it.
Q 09Which Roman general besieged Syracuse from 214 BC and later ordered that Archimedes should not be harmed?
Marcus Claudius Marcellus
He called Archimedes "a geometrical Briareus" and was reportedly angered by his death.
Q 10During which war did Syracuse switch from Rome to Carthage, prompting the siege Archimedes resisted?
The Second Punic War
The Romans took the city only after a long siege, greatly delayed by his machines.
Q 11What did Archimedes' crane-like machines reportedly do to Roman ships, per Plutarch and Livy?
Lift them out of the water with an iron claw and drop them
Other cranes dropped heavy lumps of lead onto the ships from the walls.
Q 12The story that Archimedes set Roman ships on fire with mirrors is absent from which group of writers?
The three earliest historians: Plutarch, Polybius and Livy
Galen is the first to mention mirrors; Descartes rejected the "heat ray" as false and modern reconstructions have had mixed results.
Q 13According to Livy's account, what was Archimedes doing when a Roman soldier killed him?
Q 21How many grains of sand did Archimedes conclude it would take to fill the universe?
8 × 10^63
The point was to prove that mathematics could represent arbitrarily large numbers.
Q 22Which heliocentric theorist's model does Archimedes describe in The Sand Reckoner?
Aristarchus of Samos
The Sand Reckoner is the only surviving work in which Archimedes discusses astronomy.
Q 23What was the profession of Archimedes' father Phidias, as stated in The Sand Reckoner?
Astronomer
Nothing else is known about him; Plutarch claims the family was related to King Hiero.
Drawing figures in the dust
The famous last words "Do not disturb my circles" appear in no ancient source; Valerius Maximus has him say "I beg of you, do not disturb this."
Q 14What did Archimedes ask to have placed on his tomb to represent his proudest discovery?
A sphere and a cylinder
The carving showed that a sphere's volume and surface area are two-thirds those of the enclosing cylinder.
Q 15Which Roman statesman found Archimedes' neglected tomb while quaestor on the island?
Cicero
He had it cleaned up and read some of the verses inscribed on it.
Q 16What fraction of the enclosing cylinder's volume and surface area did Archimedes show a sphere has?
Two-thirds
The sphere is 4/3 pi r cubed and the cylinder 2 pi r cubed; the ratio was his favourite result.
Q 17Between which two bounds did Archimedes show pi lies, using polygons of 96 sides?
3 10/71 and 3 1/7
He started with hexagons inside and outside a circle and doubled the sides four times.
Q 18In Quadrature of the Parabola, a parabolic segment's area is what multiple of its inscribed triangle?
4/3
He summed the geometric series 1 + 1/4 + 1/16 + ... to reach it, an early infinite series.
Q 19What technique, inherited from Eudoxus, did Archimedes use to prove areas and volumes rigorously?
The method of exhaustion
He admitted he found results first by a mechanical method using the lever, then proved them this way afterwards.
Q 20What Greek term for 10,000 did Archimedes base his large-number system on in The Sand Reckoner?
Myriad
He used powers of a myriad of myriads, that is 100 million, to count sand grains.
Q 24Which law does Archimedes prove in the first book of On the Equilibrium of Planes?
The law of the lever
It states that magnitudes balance at distances reciprocally proportional to their weights.
Q 25To which student of Conon of Samos are most of Archimedes' surviving treatises addressed?
Dositheus of Pelusium
The Method and the Cattle Problem, by contrast, were sent to the librarian Eratosthenes.
Q 26What is the Ostomachion, described in a treatise found in the Palimpsest?
A 14-piece dissection puzzle like a tangram
Reviel Netz calculated the pieces form a square in 17,152 ways, an early combinatorics problem.
Q 27Archimedes' Cattle Problem challenges Alexandrian mathematicians to count the herd of which deity?
The Sun
The hardest version's answer is roughly 7.76 × 10^206544, first solved by A. Amthor in 1880.
Q 28Who found the Cattle Problem in a 44-line Greek poem in the Herzog August Library in 1773?
Gotthold Ephraim Lessing
The German dramatist was working as the library's director at the time.
Q 29How many semiregular polyhedra did Archimedes prove exist, in a lost work described by Pappus?
Thirteen
They are still called the Archimedean solids.
Q 30What is the Archimedes Palimpsest, examined by Johan Ludvig Heiberg in Constantinople in 1906?
A prayer book written over erased copies of his treatises
It holds seven treatises, including the only surviving Greek text of On Floating Bodies.