Solve the problem.
-A rectangular swimming pool is being constructed, 18 feet long and 100 feet wide. The depth of the pool is measured at 3 -foot intervals across the length of the pool. Estimate the volume of water in the pool using the Trapezoidal Rule.
$\begin{array}{l|l}
\text { Width (ft) } & \text { Depth (ft) } \
\hline 0 & 5 \
3 & 5.5 \
6 & 6 \
9 & 7 \
12 & 7.5 \
15 & 8 \
18 & 9
\end{array}$

A) $12,300 \mathrm { ft } ^ { 3 }$
B) $8200 \mathrm { ft } ^ { 3 }$
C) $14,400 \mathrm { ft } ^ { 3 }$
D) $10,900 \mathrm { ft } ^ { 3 }$

Question

Solve the problem.
-A rectangular swimming pool is being constructed, 18 feet long and 100 feet wide. The depth of the pool is measured at 3 -foot intervals across the length of the pool. Estimate the volume of water in the pool using the Trapezoidal Rule.
$\begin{array}{l|l}
\text { Width (ft) } & \text { Depth (ft) } \
\hline 0 & 5 \
3 & 5.5 \
6 & 6 \
9 & 7 \
12 & 7.5 \
15 & 8 \
18 & 9
\end{array}$

A) $12,300 \mathrm { ft } ^ { 3 }$
B) $8200 \mathrm { ft } ^ { 3 }$
C) $14,400 \mathrm { ft } ^ { 3 }$
D) $10,900 \mathrm { ft } ^ { 3 }$

Quizplus · Accepted Answer

The volume of the pool can be estimated using the Trapezoidal Rule, which is given by the formula: $$V = \frac{d}{2} \times (w) \times (f_0 + 2f_1 + 2f_2 + \cdots + 2f_{n-1} + f_n)$$ where $d$ is the depth interval (3 feet), $w$ is the width of the pool (100 feet), and $f_0, f_1, \ldots, f_n$ are the depths at each interval. Plugging in the values from the table: $$V = \frac{3}{2} \times 100 \times (5 + 2(5.5) + 2(6) + 2(7) + 2(7.5) + 2(8) + 9)$$ $$V = 150 \times (5 + 11 + 12 + 14 + 15 + 16 + 9)$$ $$V = 150 \times 82 = 12,300 \, \text{ft}^3$$

Solve the Problem A) 12,300ft312,300 \mathrm { ft } ^ { 3 }12,300ft3

Solve the Problem A) $12,300 \mathrm { ft } ^ { 3 }$