University Physics Volume 1 — Mechanics · Problem 50

Units and Measurement — OpenStax

Physics — University · dimensional-analysis

Problem

A student is trying to remember some formulas from geometry. In what follows, assume

A

is area,

V

is volume, and all other variables are lengths. Determine which formulas are dimensionally consistent. (a)

V = \pi r^2 h

; (b)

A = 2\pi r^2 + 2\pi r h

; (c)

V = 0.5bh

; (d)

V = \pi d^2

; (e)

V = \pi d^3/6