Question

A bucket full of water in the form of a frustum of a cone whose bottom and top radii are 18 cm and 20 cm respectively and the vertical depth is 30 cm if the water in the buckets then poured into an empty cylindrical container was base radius is 20 cm find the depth of the water in the container

Answer 1

Volume of frustum = (1/3)πh(R1^2 + R1R2 + R2^2).

Here R1 = 18 cm, R2 = 20 cm, h = 30 cm:
R1^2 + R1R2 + R2^2 = 18^2 + 18·20 + 20^2 = 324 + 360 + 400 = 1084.
Volume = (1/3)π·30·1084 = 10840π cm^3.

Cylindrical container volume = π·r^2·H = π·20^2·H = 400πH.
Set equal: 400πH = 10840π ⇒ H = 10840/400 = 271/10 = 27.1 cm.

So the water depth in the cylinder is 27.1 cm.