Question

1. buckley village is installing a new water tower to improve pressure in their water system. the tank sits atop a 10m - high platform. the tank is cylindrical with a height of 3m and a diameter of 5m. the tank has a conical roof 1m high, but the water cant go into the roof.

a) if (1m^3 = 1000l), how many liters can the tank hold when full?
b) normally, the tank is filled to 85% for efficiency reasons. if the pump can add 189l per minute, how long will it take to fill the tank to 85%? (answer in minutes)

Explanation:

Step1: Find cylinder radius

The diameter is 5m, so radius $r = \frac{5}{2} = 2.5$ m

Step2: Calculate cylinder volume

Use cylinder volume formula $V = \pi r^2 h$
$V = \pi \times (2.5)^2 \times 3 = \pi \times 6.25 \times 3 = 18.75\pi \approx 58.875$ m³

Step3: Convert to liters (part a)

Since $1$ m³$=1000$ L, $58.875 \times 1000 = 58875$ L

Step4: Find 85% of tank volume

$0.85 \times 58875 = 50043.75$ L

Step5: Calculate fill time (part b)

Time = $\frac{\text{Volume to fill}}{\text{Flow rate}} = \frac{50043.75}{189} = 267.5$ minutes

Answer:

a) 58875 L
b) 267.5 minutes