5. An open water tank with length 20 cm and width 15 cm holds 4.8 litres of water. Calculate the height
of the water level in the tank and the total surface area of the cuboid in contact with the water.
6. A rectangular tank measures 4 m long, 2 m wide and 4.8 m high. Initially it is half filled with water.
Find the depth of water in the tank after 4000 litres more of water are added to it.
7. A rectangular water tank of length 60 cm and width 40 cm contains water up to a depth of 30 cm.
A piece of ice measuring 20 cm by 15 cm by 12 cm is dropped into the tank of water. Calculate the
1
new depth of water when the ice melts completely, assuming its volume decreases by
10
M.
Answers
Step-by-step explanation:
4.8 litre = 4800 cm^3 (cm cube) since 1 litre = 100cm^3
Let the height of the water level = h
Volume
= Length x width x height = 4800
20 x 15 x h = 4800
300h = 4800
h = 4800/300
h=16
Total surface area of the cuboid
= 2 ((length x width) + (length x height) + (width x height))
= 2 ((20 x 15) + (20 x 16) + (15 x 16))
= 2 (300 + 320 + 240)
= 2 (1100)
= 2200
Change 4000 liters to cu/meters: 4000/1000 = 4 cu/m
Find the initial amt of water in the tank, half full would be:
(half the given height)
4 * 2 * 2.4 = 19.2 cu/meters
Total after 4 cu/m is added to it
19.2 + 4 = 23.2 cu/m total
Find the depth (d)
4 * 2 * d = 23.2
8d = 23.2
d = 23.2%2F8
d = 2.9 meter is the depth
Check solution:
4 * 2 * 2.9 = 23.2
a rectangular water tank of length 60 cm and width 40cm contains water up to a depth of 30 cm.
A piece of ice measuring 20 cm by 15 cm by 12 cm is dropped into the tank of water.
Calculate the new depth of water when ice melts completely, assuming its volume decreases by 1/10.
Find the volume of water before the ice is added:
60 * 40 * 30 = 72000 cu cm
Find the volume of the water from the ice
.9 * 20 * 15 * 12 = 3240 cu/cm
Find the volume when the ice melts
72000 + 3240 = 75240 cu/cm
Find the new water depth (d)
d = 75240%2F%2860%2A40%29
d = 31.35 cm deep now
Check that by finding the vol of the added water. (water rose 1.35 cm)
1.35 * 60 * 40 = 3240 the vol of the melted ice