What’s the correct answer??
2 answers:
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To solve this, we are going to use the volume formula for a rectangular prism: 
where
is the volume of the prism
is the length of the prism
is the width of the prism
is the height of the prism
We are also using the volume of a sphere formula:
where
is the volume of the sphere
is the radius of the sphere
Part A: Since she <span>wants a layer of marbles in the bottom of the tank about 5 centimeters deep, the height of this little rectangular prism will be 5 centimeters, so </span>
. Since the other measures of our little rectangular prism are the same as the aquarium, 
and 
. Lets replace those values in our volume formula:
Now that we know that she wants to cover a volume of 6250
with marbles, lets find the volume of each marble.
We know that the diameter of each marble is 1 cm. Since the radius is of a sphere is half its diameter,
. Lets replace that value in our volume formula:
Now, let
the number of marbles she will need to cover a volume of 6250 :
Since we know that each bag of marbles has 500 marbles, we are going to divide the number of marbles she will need by the number of marbles in each bag:
We can conclude that to fill a layer of 5 cm with marbles, she will need 24 bags of marbles.
Part B: We know that she already have 5 cm of her aquarium filled with marbles, and that she also added water <span>until it’s level is 3 centimeters below the top of the tank, so to find the height of this new rectangular prism, we are going to subtract 5 cm plus 3 cm from the original height of her aquarium:
</span>
Since the other measures of our little rectangular prism are the same as the aquarium, and . Lets replace those values in our volume formula:
Remember that
. So:
We can conclude that there are 21.25 liters of water in the tank.
where
We are also using the volume of a sphere formula:
where
Part A: Since she <span>wants a layer of marbles in the bottom of the tank about 5 centimeters deep, the height of this little rectangular prism will be 5 centimeters, so </span>
Now that we know that she wants to cover a volume of 6250
We know that the diameter of each marble is 1 cm. Since the radius is of a sphere is half its diameter,
Now, let
Since we know that each bag of marbles has 500 marbles, we are going to divide the number of marbles she will need by the number of marbles in each bag:
We can conclude that to fill a layer of 5 cm with marbles, she will need 24 bags of marbles.
Part B: We know that she already have 5 cm of her aquarium filled with marbles, and that she also added water <span>until it’s level is 3 centimeters below the top of the tank, so to find the height of this new rectangular prism, we are going to subtract 5 cm plus 3 cm from the original height of her aquarium:
</span>
Since the other measures of our little rectangular prism are the same as the aquarium,
Remember that
We can conclude that there are 21.25 liters of water in the tank.
The standard form is pretty much the variables on the left-hand-side and the constant alone by herself on the right-hand-side, with only positive integers on the x-variable and an integers all around.
