The engine in a car has eight cylinders. Each cylinder is a right cylinder with a diameter of 3.032 inches and a height of 6 inches. Find the total displacement (volume) of this engine.
The volume of one cylinder is:
V = πr^2h
where r is the radius (half of the diameter) and h is the height.
r = 3.032/2 = 1.516 inches
V = π(1.516)^2(6) = 42.97 cubic inches
The total displacement of the engine is:
8 cylinders x 42.97 in^3/cylinder = 343.76 in^3
Therefore, the total displacement of the engine is 343.76 cubic inches.
To find the total displacement (volume) of the engine, we need to compute the volume of each cylinder and then multiply it by the total number of cylinders.
The volume of a right cylinder can be calculated using the formula:
Volume = π * r^2 * h
where r is the radius (half the diameter) and h is the height.
Given that the diameter of each cylinder is 3.032 inches, the radius (r) can be calculated by dividing the diameter by 2:
r = 3.032 / 2 = 1.516 inches
The height (h) of each cylinder is given as 6 inches.
Substituting these values into the formula, we can calculate the volume of each cylinder:
Volume of 1 cylinder = π * (1.516)^2 * 6 cubic inches
Now we need to multiply this volume by the total number of cylinders, which is 8:
Total displacement of the engine = Volume of 1 cylinder * Total number of cylinders
Let's calculate it step by step:
Step 1: Calculate the radius of each cylinder:
r = 3.032 / 2 = 1.516 inches
Step 2: Calculate the volume of one cylinder:
Volume of 1 cylinder = π * (1.516)^2 * 6 cubic inches
=~ 3.1416 * (1.516)^2 * 6 cubic inches
Step 3: Calculate the total displacement of the engine:
Total displacement of the engine = Volume of 1 cylinder * Total number of cylinders
= (3.1416 * (1.516)^2 * 6 cubic inches) * 8
Now, you can calculate the final answer.