Question

a chemistry student in lab needs to fill a temperature - control tank with water. the tank measures 34.0 cm long by 12.0 cm wide by 8.0 cm deep. in addition, as shown in the sketch below, the student needs to allow 2.0 cm between the top of the tank and the top of the water, and a round bottom flask with a diameter of 5.5 cm will be just barely submerged in the water. calculate the volume of water in liters which the student needs. round your answer to the nearest 0.01 l.

Explanation:

Step1: Calculate the height of water

The tank's total depth is 8.0 cm, and there's 2.0 cm from water top to tank top, so water height \( h = 8.0 - 2.0 = 6.0 \) cm. Also, the flask has diameter 5.5 cm, so radius \( r = \frac{5.5}{2} = 2.75 \) cm.

Step2: Volume of water (tank - flask volume)

Tank volume (rectangular): \( V_{tank} = l \times w \times h = 34.0 \times 12.0 \times 6.0 \) \( = 2448 \) \( cm^3 \).
Flask volume (cylinder): \( V_{flask} = \pi r^2 h = \pi \times (2.75)^2 \times 6.0 \) \( \approx 139.89 \) \( cm^3 \).
Water volume: \( V = V_{tank} - V_{flask} = 2448 - 139.89 = 2308.11 \) \( cm^3 \).

Step3: Convert to liters

Since \( 1 L = 1000 cm^3 \), \( V = \frac{2308.11}{1000} = 2.30811 \) L, rounded to nearest 0.01 L is 2.31 L.

Answer:

2.31