A certain marine engine has cylinders that are 3.72 cm in diameter and 5.35 cm deep. Find the total volume of 8 cylinders​ (Use 3.14 for pi as needed. Round to the nearest​ hundredth).

Question content area bottom
Part 1
A.
999.88 cm3
B.
929.89 cm3
C.
464.94 cm3
D.
58.12 cm3

1 answer

To find the total volume of 8 cylinders, we first need to find the volume of a single cylinder using the formula for the volume of a cylinder:

\[ V = \pi r^2 h \]

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height (or depth) of the cylinder.

  1. Calculate the radius: The diameter of the cylinder is 3.72 cm, so the radius \( r \) is half of that:

    \[ r = \frac{3.72}{2} = 1.86 , \text{cm} \]

  2. Height of the cylinder: The height \( h \) is given as 5.35 cm.

  3. Substitute the values into the volume formula: Using \( \pi = 3.14 \):

    \[ V = 3.14 \times (1.86)^2 \times 5.35 \]

    Now we calculate \( (1.86)^2 \):

    \[ (1.86)^2 = 3.4596 \]

    Now substitute this value back into the volume formula:

    \[ V = 3.14 \times 3.4596 \times 5.35 \]

    Calculate \( 3.14 \times 3.4596 \):

    \[ 3.14 \times 3.4596 \approx 10.852784 \]

    Now multiply by 5.35:

    \[ V \approx 10.852784 \times 5.35 \approx 58.1125 , \text{cm}^3 \]

  4. Calculate the total volume for 8 cylinders:

    \[ \text{Total Volume} = 8 \times V \] \[ \text{Total Volume} \approx 8 \times 58.1125 \approx 464.9 , \text{cm}^3 \]

Finally, rounding this to the nearest hundredth:

\[ \text{Total Volume} \approx 464.94 , \text{cm}^3 \]

Therefore, the answer is C. 464.94 cm³.