Mathematics, 26.07.2019 19:00 jaqwannewsome

Stephanie has an aquarium that is in the shape of a right rectangular prism, 50 centimetres long, 25 centimetres wide and 30 centimetres y’all. for decoration, strong wants a layer of marbles in the bottom of the tank about 5 centimetres deep. the marbles have a diameter of 1 centimeter and come in bags of 500. part a: how many bags of marble will stephanie need? part b: stephanie pours all of the marbles into the tank. she now adds water until it’s level 3 centimetres below the top of the tank. how much water is in the tank? express your answer in liters

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Answer from: terrenevans4156

To solve this, we are going to use the volume formula for a rectangular prism: V=lwh

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: $V= \frac{4}{3} \pi r^{3}$
where

is the volume of the sphere

is the radius of the sphere

Part A: Since she 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 h=5

. Since the other measures of our little rectangular prism are the same as the aquarium, l=50

and

. Lets replace those values in our volume formula:
V=lwh

$V=6250 cm^{3}$
Now that we know that she wants to cover a volume of 6250 $cm^{3}$ 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, $r= \frac{1}{2} =0.5$ . Lets replace that value in our volume formula:
$V= \frac{4}{3} \pi r^{3}$
$V= \frac{4}{3} \pi (0.5)^{3}$
$V=0.52 cm^{3}$
Now, let

the number of marbles she will need to cover a volume of 6250 $cm^{3}$ :
0.52x=6250

$x= \frac{6250}{0.52}$
x=12019.23

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:
$\frac{12019.23}{500} =24.03$

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 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:
h=30-(5+8)

Since the other measures of our little rectangular prism are the same as the aquarium, l=50

and

. Lets replace those values in our volume formula:
V=lwh

$V=21250cm^{3}$
Remember that $1litre=1000cm^{3}$ . So:
$(21250cm^3)( \frac{1litre}{1000cm^{3})} =21.25liters$

We can conclude that there are 21.25 liters of water in the tank.

Answer from: Quest

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

Answer from: Quest

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000 [12% converted to decimal as 0.12]

= $3720