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PEAZIT Aha card

A sphere: surface squares the radius, volume cubes it

A sphere's surface is four times the area of its largest circular cross-section. Its volume is V = 4πr³/3.

With r = 3 cm the numerical results coincide, but the units differ.

Relation	Meaning
S = 4πr²	Surface area uses r².
V = 4πr³ / 3	Volume uses r³ and division by three.
r = 3: S ≈ 113.04; V ≈ 113.04	The numerical equality here is coincidental.

One worked example

S = 4πr²Surface area uses r².
V = 4πr³ / 3Volume uses r³ and division by three.
r = 3: S ≈ 113.04; V ≈ 113.04The numerical equality here is coincidental.

Watch out: Radius is not diameter. Volume and surface area measure different quantities.

Goal, prerequisites and card origin

What you will learn: Distinguish sphere surface and volume formulas.

What you need first: Radius, squares and cubes.

An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1

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A sphere's surface is four times the area of its largest circular cross-section. Its volume is V = 4πr³/3.

Without JavaScript, write your answer elsewhere before opening the solution.A sphere has radius 2 cm. Using π = 3.14, find its surface area in cm². Enter a number.

Solution — open after your own attempt

50.24 4 × 3.14 × 2² = 50.24 cm².

A question for your next return: A sphere has radius 6 cm. Using π = 3.14, find its volume in cm³. Enter a number.

Solution — open after your own attempt

904.32 4 × 3.14 × 216 / 3 = 904.32 cm³.

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