A cylinder shaped fish talk is 40cm high and has a radius of 12cm.
The tank with be layed with a decorative gravel on the bottom.
The blue layer will be 2 cm high.
The yellow layer will be 3 cm high.
And the green layter will be 2cm high.
[assume water won't go through the gravel...okay?]
Find the number of liters of water (1000 cubic CM = 1 L) needed to fill the tank to a level that is one CM from the top before the fish are put into the tank.
*Like, what method should i use? HOW? and whats the volume formula again?? HELP.
http://www.mathsteacher.com.au/year9/ch14_measurement/18_cylinder/cylinder.htm
To find the volume of water needed to fill the tank, you will need to calculate the volume of the cylinder and subtract the volume occupied by the decorative gravel layers.
The volume of a cylinder is calculated using the formula: V = π * r^2 * h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius, and h is the height.
In this case, the height of the cylinder-shaped fish tank is given as 40cm, and the radius is given as 12cm.
Step 1: Calculate the volume of the cylinder:
V_cylinder = π * r^2 * h
V_cylinder = 3.14 * (12cm)^2 * 40cm
V_cylinder = 3.14 * 144cm^2 * 40cm
V_cylinder = 18096cm^3
Step 2: Calculate the volume occupied by the decorative gravel layers:
Volume of blue layer = area of the base * height = π * r^2 * 2cm
Volume of yellow layer = area of the base * height = π * r^2 * 3cm
Volume of green layer = area of the base * height = π * r^2 * 2cm
To find the total volume of the decorative gravel layers, add the volumes of each layer together.
V_gravel = (π * r^2 * 2cm) + (π * r^2 * 3cm) + (π * r^2 * 2cm)
V_gravel = π * r^2 * (2cm + 3cm + 2cm)
V_gravel = π * 144cm^2 * 7cm
V_gravel = 3172.64cm^3
Step 3: Calculate the volume of water needed:
Volume of water = Volume of the cylinder - Volume of the gravel layers
Volume of water = V_cylinder - V_gravel
Volume of water = 18096cm^3 - 3172.64cm^3
Volume of water = 14923.36cm^3
Finally, to convert the volume from cubic centimeters (cm^3) to liters (L), divide by 1000 (since 1000 cubic cm = 1 L):
Volume of water (in liters) = Volume of water (in cm^3) / 1000
Volume of water (in liters) = 14923.36cm^3 / 1000
Volume of water (in liters) ≈ 14.92L
Therefore, approximately 14.92 liters of water are needed to fill the tank to a level that is one centimeter from the top before the fish are put into the tank.