The given cylindrical container r =3 inches and height= 8in is used to fill the rectangular prism fish tank 24 , 24 and 12 inches with water. What is the least number of full cylindrical needed to completely fill the fish tank?
cylinder = 226.08
rectangular Prism = 6912
= 6912/226.08
=30.573
Volume of a cylinder:
V=π*r^2*h
V = 3.14 * 3 * h
V = ?
Volume of a rectangular prism:
V=whl
V = 24 * 24 * 12
V = ?
Right.
To find the least number of full cylinders needed to completely fill the fish tank, we need to determine the volume of both the cylindrical container and the fish tank.
First, let's find the volume of the cylindrical container. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
In this case, the radius (r) of the cylindrical container is given as 3 inches, and the height (h) is given as 8 inches. So, the volume of the cylindrical container is:
V_cylinder = π(3^2)(8) = 72π cubic inches
Next, let's find the volume of the fish tank. The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length (l) of the fish tank is given as 24 inches, the width (w) is also 24 inches, and the height (h) is 12 inches. So, the volume of the fish tank is:
V_fish tank = (24)(24)(12) = 6912 cubic inches
Now, we can divide the volume of the fish tank by the volume of the cylindrical container to find the number of cylinders needed:
Number of cylinders = V_fish tank / V_cylinder
Number of cylinders = 6912 / (72π)
Using a calculator, we can compute this value:
Number of cylinders ≈ 29.68
Since we cannot have a fraction of a cylinder, we need to round up the number to the nearest whole number:
Number of cylinders = 30
Therefore, the least number of full cylinders needed to completely fill the fish tank is 30.