Question

The pond is completely full of water. Sumeet wants to
empty the pond so he can clean it. Sumeet uses a pump to empty
the pond. The volume of water in the pond decreases at a constant
rate. The level of the water in the pond goes down by 20cm in the
first 30 minutes. Work out how much more time Sumeet has to
wait for the pump to empty the pond completely.

Answer 1

Answer:

40MIN

Step-by-step explanation:

Answer 2

Recall:

$\text{Area of a trapezoid } = \dfrac{1}{2} \times (a + b) \times h \\\text{ where a and b are the two parallel lines and h, the height}$

$\text{Volume } = \text{Base Area } \times \text {height}$

Find the area of the cross-section:

The area of the cross-section is the area of a trapezoid.

$\text{Area of a trapezoid } = \dfrac{1}{2} \times (a + b) \times h$

$\text{Area of a trapezoid } = \dfrac{1}{2} \times (1.3 + 0.5) \times 2$

$\text{Area of a trapezoid } = 1.8 \text { m}^2$

Find the volume of the pond:

$\text{Volume } = \text{Base Area } \times \text {height}$

$\text{Volume } = 1.8 \times 1$

$\text{Volume } = 1.8 \text{ m}^3$

Convert m³ to cm³:

$1.8. \text{ m}^3 = 1.8 \times 100 \times 100 \times 100 \text{ cm}^3$

$1.8. \text{ m}^3 = 1800000 \text{ cm}^3$

Find the amount of water drained in the first 30 mins:

$20 \text { cm} = 0.2 \text { m}$

$\text{Volume }= \text{Length} \times \text{Breadth} \times \text{Height}$

$\text{Volume }= 2 \times 1 \times 0.2$

$\text{Volume }= 0.4 \text{ m}^3$

Find the amount of water left:

$\text{Volume Left} = 1.8 - 0.4$

$\text{Volume Left} = 1.4 \text{ m}^3$

Find the amount of time needed to drain the water left:

$0.4 \text { m}^3 = 30 \text { mins}$

$1 \text { m}^3 = 30 \div 0.4$

$1 \text { m}^3 = 75 \text { mins}$

$1.4 \text { m}^3 = 75 \times 1.4$

$1.4 \text { m}^3 = 105 \text { mins}$

$1.4 \text { m}^3 = 1 \text{ hour } 45 \text { mins}$

Answer: She needs to wait for another 1 hour 45 mins to finish draining the pond.