SOLUTION: Hi a container has a rectangular base with a length twice its breadth. Its height is 30cm. It is 1/3 full. 3000cm^2 of water is then added and the new height is 25cm. 1) How mu

Question 1201743: Hi
a container has a rectangular base with a length twice its breadth. Its height is 30cm. It is 1/3 full. 3000cm^2 of water is then added and the new height is 25cm.
1) How much more water is needed to fill the tank to its brim
2) what is the length of the container.
Thanks
Found 4 solutions by mananth, math_tutor2020, ikleyn, greenestamps:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
CHECK your problem . There appears to be some error
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answers:
1 liter of water is needed
length = 20 cm

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Work Shown:

x = breadth
2x = length
area of base = length*breadth
area of base = 2x*x
area of base = 2x^2

h = starting height of the water line
volume of water = (area of base)*(height of water line)
volume of water = (2x^2)*(h)
volume of water = 2x^2h

volume of the tank = (area of the base)*(height of the tank)
volume of the tank = 2x^2*30
volume of the tank = 60x^2

When the tank is 1/3 full, there are 2x^2h cubic cm of water.

volume of water = (1/3)*(volume of tank)
2x^2h = (1/3)*(60x^2)
2x^2h = 20x^2
2h = 20
h = 20/2
h = 10

The water line starts off at a height of 10 cm.
The shortcut would be to say (1/3)*30 = 10.

After adding the 3000 cm^3 of water, the height goes to 25 cm.
Which is an increase of 25-10 = 15 cm.

new amount of water = (area of base)*(change in height)
new amount of water = (2x^2)*(15)
new amount of water = 30x^2

This is set equal to 3000 since we've added this new amount of water.
30x^2 = 3000
x^2 = 3000/30
x^2 = 100
x = sqrt(100)
x = 10
then
2x = 2*10 = 20

The breadth is 10 cm.
The length is 20 cm.
The area of the base is 20*10 = 200 cm^2

The tank is 30 cm tall and we've reached the 25 cm marker
The difference in height is 30-25 = 5 cm.

Let's calculate how much water we need to fill up the rest of the tank.
water needed = (area of the base)*(change in height)
water needed = (200)*(5)
water needed = 1000 cm^3
water needed = 1000 mL
water needed = 1 liter

Answer by ikleyn(52855)   (Show Source): You can put this solution on YOUR website!
.
a container has a rectangular base with a length twice its breadth. Its height is 30cm.
It is 1/3 full. 3000cm^2 of water is then added and the new height is 25cm.
1) How much more water is needed to fill the tank to its brim
2) what is the length of the container.
~~~~~~~~~~~~~~~~~~

Hey, for your info:

The volume, and the volume of water, in particular, is not measured in square centimeters,
as it is stated in your post.

It is a fatal error. Inform your professor to fix it.

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

I think we can call the "3000 cm^2" in the problem a typographical error instead of a fatal flaw. Obviously the intent was 3000 cm^3....

The height is 30cm, and initially the tank is 1/3 full, so it is filled to a depth of 10cm.

When 3000 cm^3 of water is added, the depth of water in the tank becomes 25cm, a change of 15cm. Since the change in the depth of the water is half the height of the tank, the 3000 cm^3 that was added is half the volume of the tank. So the volume of the tank is 6000 cm^3.

1) How much more water is needed to fill the tank to its brim?

The water is now 5cm from the top of the tank. Since adding 3000 cm^3 raised the depth of the water by 15cm, the additional amount of water needed to raise the depth of the water another 5cm is one-third of 3000 cm^3, or 1000 cm^3.

ANSWER: 1000 cm^3

2) what is the length of the container?

The volume of the tank is 6000 cm^3, and the height is 30cm; that means the area of the rectangular base is 200 cm^2. Then, since the length is twice the width, the length of the base is 20cm and the width is 10cm.

ANSWER: 20cm

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