A rectangular tank measures 60cm by 40cm by 30cm. It is half filled with water. Water is added to the tank at a rate of 13litres per minute and drained out at 9litres per minute. Find the volume of water in the tank after 7 minutes.
You already have 60x40x15
or 36000 cm^3 in the half-filled tank
or you have 36 L in the half-filled tank
The net increase from that point on is 4 L/min
So in the next 7 minutes, 28 L are added
Total volume = 36+28 = 64 L
thanks, just double checking to see if i got it right.
calculate the perimeter of the area that is shaded in the diagram of a semi-circle fitted in a rectangle
To find the volume of water in the tank after 7 minutes, we need to calculate the net change in the volume.
First, let's calculate the initial volume of water in the tank. The tank is half-filled with water, so the initial volume of water is (1/2) * (60cm) * (40cm) * (30cm) = 36,000 cm³.
Next, let's calculate the net change in volume over the 7 minutes.
Water is being added to the tank at a rate of 13 litres per minute. To convert litres to cubic centimeters (cm³), we need to multiply by 1000 (1 litre = 1000 cm³). Therefore, the addition rate is 13 * 1000 = 13,000 cm³ per minute.
Water is also being drained out of the tank at a rate of 9 litres per minute. So, the drainage rate is 9 * 1000 = 9,000 cm³ per minute.
Since water is being added faster than it is being drained, the net change in volume per minute is the addition rate minus the drainage rate:
Net change in volume per minute = 13,000 cm³/min - 9,000 cm³/min = 4,000 cm³/min.
To find the net change in volume over 7 minutes, we multiply the net change per minute by the number of minutes:
Net change in volume over 7 minutes = 4,000 cm³/min * 7 min = 28,000 cm³.
Finally, to find the volume of water in the tank after 7 minutes, we add the net change in volume to the initial volume:
Volume of water after 7 minutes = 36,000 cm³ + 28,000 cm³ = 64,000 cm³.
Therefore, the volume of water in the tank after 7 minutes is 64,000 cm³.