Raymond built a rocket made from a cylinder and a cone. He filled the rocket completely with water: what is the maximum number of gallons of water the rocket can hold? Find your answer in terms of pie and using 3.14 for pie: (231 in^3 = 1 gallon)
To find the maximum number of gallons of water the rocket can hold, let's first find the total volume of the rocket.
The rocket is made up of a cylinder and a cone. The volume of a cylinder is given by the formula V_cylinder = πr^2h, where r is the radius of the base and h is the height.
The volume of a cone is given by the formula V_cone = (1/3)πr^2h, where r is the radius of the base and h is the height.
Since the rocket is completely filled with water, the total volume of the rocket is the sum of the volume of the cylinder and the volume of the cone.
Let's say the radius of the base of the cylinder is r_cylinder and the height of the cylinder is h_cylinder. Similarly, let's say the radius of the base of the cone is r_cone and the height of the cone is h_cone.
The total volume of the rocket is:
V_rocket = V_cylinder + V_cone
V_rocket = πr_cylinder^2h_cylinder + (1/3)πr_cone^2h_cone
Now, let's substitute the given values and calculate the volume.
Using the value 3.14 for π:
V_rocket = 3.14 * r_cylinder^2 * h_cylinder + (1/3) * 3.14 * r_cone^2 * h_cone
To find the maximum number of gallons of water the rocket can hold, we need to convert the volume to gallons.
We know that 231 in^3 = 1 gallon.
So, the maximum number of gallons of water the rocket can hold is:
(V_rocket / 231) gallons