Question

Using polar coordinates, find the volume of the cylinder with radius a and height h.

(a) \(πa^2h \)

(b) \(\frac{πa^2h}{3} \)

(c) \(2 \frac{πa^2h}{3} \)

(d) \( 4 \frac{πa^2h}{3} \)

The question was posed to me during a job interview.

Query is from Volume Integrals in division Vector Integral Calculus of Engineering Mathematics

Answer 1

Right option is (a) \(πa^2h \)

Best explanation: r: 0 to a

θ : 0 to 2 π

z: 0 to h

Therefore, volume = \(\int_0^a \int_0^{2π}\int_0^h rdθdrdz \)

\(= (\int_0^a rdr)(\int_0^{2π}dθ)(\int_0^h dz) \)

\(= \frac{a^2}{2} * 2π * h \)

\(= πa^2h. \)