Question

Help me guys!!

A rectangular tank with a square base in initially contained 2.6 litersof water. A cube of edges 15 cm was full of water. The water from the cubic container was poured into the tank until it was completely filled. There were 95 cubic cm of water left in the cube. (1L = 1000 cm³) a) If the height of the rectangular tank is 30 cm, find the length of its base.
b) Water from the tank was then drained out at a rate of 0.49 liter per minute. Find the time taken to empty the tank.​

Answer 1

a) Since the rectangular tank has a square base, let's assume that the length of the base is x cm. Then, the area of the square base is x² cm². The volume of the rectangular tank is given by:

Volume of tank = Base area x Height

Substituting the given values, we get:

2.6 L = 2600 cm³
Volume of tank = x² cm² x 30 cm = 30x² cm³

When the cube is emptied into the tank, the volume of water in the tank becomes:

Volume of water in tank = 2600 cm³ + 15000 cm³ - 95 cm³
Volume of water in tank = 17505 cm³

Since the tank is completely filled with water, the volume of water in the tank is equal to the volume of the tank:

30x² cm³ = 17505 cm³

Solving for x, we get:

x = √(17505/30) cm
x = 21 cm (rounded to the nearest whole number)

Therefore, the length of the base of the rectangular tank is 21 cm.

b) The volume of water in the tank is 17505 cm³. To find the time taken to empty the tank, we can use the formula:

Time = Volume / Rate

Substituting the given values, we get:

Time = 17505 cm³ / (0.49 L/min x 1000 cm³/L)
Time = 35.7 min (rounded to one decimal place)

Therefore, the time taken to empty the tank is 35.7 minutes.

Answer 2

a) 14 cm

b) 12 minutes

Explanation:

Rectangular tank with square base:

Initial water in the container = 2.6 liter

To convert 2.6 l to cubic cm, multiply 2.6 by 1000.

= 2.6 *1000

= 2600 cubic cm

Now, let us find the capacity of the cubic container with edge 15 cm.

`\boxed{ \text {\bf Volume of cube = $edge^3$}}`

`\sf = 15 * 15 * 15\\\\ = 3375 \ cm^3`

In 3375 cubic cm of water, only 95 cubic cm is left. To find the water that is transferred into the rectangular tank subtract.

Water transferred into the rectangular tank = 3375 - 95

= 3280 cubic cm

To find the full capacity of the tank, add the initial capacity water in the tank with 3280 cubic cm.

Full capacity of the tank = 3280 + 2600

= 5880 cubic cm

`\boxed{\text{\bf Volume of rectangular tank with square base = area of the base * h = edge^2 * h}}` Volume of rectangular tank with square base = area of base * height

`\boxed{\text{\bf Volume of rectangular tank with square base = $edge^2*h$}}`

`\sf edge^2 * h = 5880 \ cm^3\\\\ edge^2 * 30 = 5880\\\\~~~~~~ edge^2 = (3880)/(30)\\\\\\~~~~~~ edge^2 = 196\\\\~~~~~~ edge ~~ = √(196)\\\\~~~~~~ edge ~~ = 14 \ cm`

`\boxed{\text{\bf length of the base = 14 \ cm}}`

b) Time taken to drain 0.49 liters of water = 1 minute

Time taken to drain 5.88 liters of water = 5.88 ÷0.49

= 12 minutes