Guesstimates

A guesstimate is a sensible estimate when exact data are missing. The steps: guess first, then model, assume, approximate and calculate.

Golgappas. 5000π cm³ of pani ÷ the pani in one golgappa. Different sizes and fillings gave about 1850 and about 870. Both are reasonable: the answer depends on the assumptions, so always say what you assumed.

Packing balls. Dividing a room's volume by a ball's volume gives an upper bound (too many), because round balls leave gaps. Ball-on-ball stacking fills about 52% of the space; nesting each layer in the hollows of the one below can fill about 74%.

The thirsty crow. Dropping a solid into water raises the water by the solid's volume. To raise water 4 cm in a glass of radius 4 cm needs 64π cm³ ÷ (4/3)π cm³ = 48 marbles of radius 1 cm.

Volumes scale as r³. Jupiter's radius is about 11 times Earth's, so it holds about 11³ ≈ 1300 Earths; the Sun holds about 13 lakh.

Thin layers: volume ≈ area × thickness. All the Earth's water spread evenly over the Earth would be about 1.38 × 10⁹ ÷ 5.1 × 10⁸ ≈ 2.7 km deep.