Question

Find the volume of the cylinder, in cubic meters. Use 3.14 for pi. Round your answer to the nearest hundredth. 10cm 4cm and 7cm

Answer 1

To find the volume of a cylinder, the formula is:

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

where \( r \) is the radius and \( h \) is the height of the cylinder. Based on the dimensions you provided (10 cm, 4 cm, and 7 cm), we need to identify which value corresponds to the height and which one corresponds to the diameter (from which we can find the radius).

- If we consider 10 cm to be the diameter, then the radius \( r \) is half of that:

\[
r = \frac{10 \, \text{cm}}{2} = 5 \, \text{cm}
\]

- The height \( h \) can be either 4 cm or 7 cm.

Let's calculate the volume using both possibilities for the height.

1. **Using height = 4 cm**:

\[
V = 3.14 \times (5 \, \text{cm})^2 \times 4 \, \text{cm}
\]

\[
V = 3.14 \times 25 \, \text{cm}^2 \times 4 \, \text{cm}
\]

\[
V = 3.14 \times 100 \, \text{cm}^3
\]

\[
V = 314 \, \text{cm}^3
\]

2. **Using height = 7 cm**:

\[
V = 3.14 \times (5 \, \text{cm})^2 \times 7 \, \text{cm}
\]

\[
V = 3.14 \times 25 \, \text{cm}^2 \times 7 \, \text{cm}
\]

\[
V = 3.14 \times 175 \, \text{cm}^3
\]

\[
V = 549.5 \, \text{cm}^3
\]

Now, we need to convert the volume from cubic centimeters to cubic meters (since \( 1 \, \text{m}^3 = 1,000,000 \, \text{cm}^3 \)):

1. For 314 cm³:

\[
V = \frac{314 \, \text{cm}^3}{1,000,000} = 0.000314 \, \text{m}^3
\]

2. For 549.5 cm³:

\[
V = \frac{549.5 \, \text{cm}^3}{1,000,000} = 0.0005495 \, \text{m}^3
\]

Finally, rounding both volumes to the nearest hundredth in cubic meters:

- \( 0.000314 \, \text{m}^3 \) rounds to \( 0.00 \, \text{m}^3 \).
- \( 0.0005495 \, \text{m}^3 \) also rounds to \( 0.00 \, \text{m}^3 \).

Thus, depending on the height chosen, the rounded volumes are both \( 0.00 \, \text{m}^3 \) when expressed to the nearest hundredth.