Question

17
the diagram shows a cross - section of a swimming pool which is 25 m long, 1 m deep at the shallow end and 2 m deep at the deep end.
(a) calculate the area of the cross - section in m².
(b) given that the swimming pool is 10 m wide, calculate the volume of the pool in m³.
answer (a) ____________ m²
(b) ____________ m³

Explanation:

Step1: Identify the shape of cross - section

The cross - section of the swimming pool is a trapezoid with parallel sides $a = 1$ m and $b = 2$ m and height $h = 25$ m.

Step2: Calculate the area of the trapezoid

The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$. Substitute $a = 1$, $b = 2$, and $h = 25$ into the formula: $A=\frac{(1 + 2)\times25}{2}=\frac{3\times25}{2}=37.5$ $m^{2}$.

Step3: Calculate the volume of the pool

The volume $V$ of the pool is the product of the cross - sectional area $A$ and the width $w$ of the pool. Given $A = 37.5$ $m^{2}$ and $w=10$ m, then $V=A\times w=37.5\times10 = 375$ $m^{3}$.

Answer:

(a) $37.5$
(b) $375$