Question

The deck of a ship is 35m long. At equal intervals of 5m the width is given by the following table: Width (m) 0 2.9 5.1 6.5 5.9 4.1 3.0 2.3 Estimate the area of the deck.

Answer 1

The area of the deck will be 140.5 m²

Explanation

The width is given by the table:   0   2.9   5.1   6.5   5.9   4.1   3.0   2.3

For finding the area of the deck, we need to use Simpson's Rule. The formula is......

$A= \frac{n}{3}[(a_{1}+a_{8})+4(a_{2}+a_{4}+a_{6})+2(a_{3}+a_{5}+a_{7})]$

here, A is the area,  'n' is the interval and a₁ to a₈ are the values of widths given in the table.

So,  n = 5 and  a₁ = 0,  a₂ = 2.9,  a₃ = 5.1,  a₄ = 6.5,  a₅ = 5.9,  a₆ = 4.1,  a₇ = 3.0 and a₈ = 2.3

Plugging these values into the above formula, we will get......

$A=\frac{5}{3}[(0+2.3)+4(2.9+6.5+4.1)+2(5.1+5.9+3.0)]\\ \\ A= \frac{5}{3}[2.3+4(13.5)+2(14)]\\ \\ A= \frac{5}{3}[2.3+54+28]\\ \\ A=\frac{5}{3}[84.3]=140.5$

So, the area of the deck will be 140.5 m²

Answer 2

A =i/3 [(a₁ + a₈) + 4(a₂ +a₄ + a₆) + 2 (a₃ + a₅ + a₇)] This will be our equation 1

Here A is the area we are trying to find.

I is the interval

And a is the values of the width

And when we apply the equation 1 we will get:

A = 5/3 [(0 + 2.3) + 4 (2.8 + 6.5 + 4.1) + 2(5.2 + 5.8 + 3)]

So when we solve this equation we will get this:

A = 5/3 [2.3 + 53.6 + 28]

= 5/3 x 83.9 ≈ 139.83

So the required area is 139.83

Note: We used the Simpson's Rule in this question.