math 1012 college

Question

The size of an engine is a measure of volume. To calculate the size of an engine is to find the volume of a cylinder and multiply by the number of cylinders. The size of a cylinder is given as a bore size, or diameter, and a stroke size, or height, of the cylinder.

Find the size of an 8-cylinder Chevy big-block engine with a bore of 4.25 inches and a stroke of 3.76 inches. Round to the nearest hundredth and use 3.14 for 

.

The size of the engine is 

 cubic inches.

Answer 1

The volume of a cylinder is V=π(r^2)h

In our problem, we are told that...

- bore size is the same as a diameter (D)

-stroke size is the same as our height (h).

-we need to use 3.14 for Pi

For our equation, we need to know the radius and the height.

We are already given a height of 3.76 inches.

h=3.76

We are not, however, given the radius (r). But, we can find the radius(r) by dividing our diameter (bore size or D) of 4.25 inches by 2.

r = D/2

r = 4.25 inches / 2

r = 2.125 inches

Now that we have both our radius (r) and our height (h) we can plug our numbers into our equation to find the volume (v) of ONE cylinder.

V=(3.14)(2.125 inches ^2)(3.67 inches)

V=(3.14)(4.5156 inches squared)(3.67 inches)

V= (3.14)(16.573 inches cubed)

V= 52.0371 inches cubed

The volume of one cylinder is 52.0371 inches cubed, but we are also told that our engine has 8 cylinders so we will need to multiply our volume (v) by 8.

V= (52.0371 inches cubed)(8)

V = 416.2972 inches cubed

Now that we have the total volume of the engine we need to round to the nearest hundredth. This would be to the second decimal place.

V = 416.30 inches cubed.

The total volume of our engine rounded to the nearest hundredth place is 416.30 inches cubed.