Question

The areas of equidistantly spaced sections of the underwater form of a small boat are as follows:1.76, 2.78, 3.10, 3.12, 2.61, 1.24, 0.85m2 . Determine the underwater volume if the sections are 3m apart

Answer 1

We will use Simpson's rule to find the volume.

The Simpson's formula is as follows :

Vol = h/3(A₁ + 2A₂ + 4A₃ + 2A₄ + 4 A₅ + 2A₆ + 4A₇)

h = 3

Vol = 3/3(1.76 + 2 × 2.78 + 4 × 3.10 + 2 × 3.12 + 4 × 2.61 + 2 × 1.24 + 4 × 0.85)

= 1.76 + 5.56 + 12.4 + 6.24 + 10.44 + 2.48 + 3.4

= 42.28

= 42.28 m³

Answer 2

Here we will use Simpson's rule to find the volume underwater.

The Simpson's formula is as follows:

Volume underwater = h/3(A₁ + 2A₂ + 4A₃ + 2A₄ + 4 A₅ + 2A₆ + 4A₇)

h = 3

Volume underwater = 3/3(1.76 + 2 × 2.78 + 4 × 3.10 + 2 × 3.12 + 4 × 2.61 + 2 × 1.24 + 4 × 0.85)

= 1.76 + 5.56 + 12.4 + 6.24 + 10.44 + 2.48 + 3.4

= 42.28m^3