To find the volume of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
Where:
- \(V\) is the volume,
- \(\pi\) is a constant (approximately 3.14),
- \(r\) is the radius of the base of the cylinder,
- \(h\) is the height of the cylinder.
From your information:
- The height (h) is 5 cm.
- The diameter is given as 8.3 cm, which means the radius (r) is half of the diameter:
\[ r = \frac{8.3}{2} = 4.15 \text{ cm} \]
Now, plug these values into the volume formula:
\[ V = 3.14 \times (4.15)^2 \times 5 \]
Calculating \((4.15)^2\):
\[ (4.15)^2 = 17.2225 \]
Now substitute back into the volume formula:
\[ V = 3.14 \times 17.2225 \times 5 \]
Calculating \(3.14 \times 17.2225\):
\[ 3.14 \times 17.2225 \approx 54.05135 \]
Now multiply by 5:
\[ V \approx 54.05135 \times 5 \approx 270.25675 , \text{cm}^3 \]
Since the answer choices you provided are in cubic meters, you need to convert cubic centimeters to cubic meters:
\[ 1 \text{ m}^3 = 1,000,000 \text{ cm}^3 \]
To convert the volume from cm³ to m³:
\[ 270.25675, \text{cm}^3 = \frac{270.25675}{1,000,000} \approx 0.00027025675 , \text{m}^3 \]
However, this does not match any of the provided answers.
Let’s verify with the response choices. It seems that there might be a discrepancy due to the unit conversions. The volume computed is significantly less than the options given (in cubic meters).
Could you confirm if the cylinder's dimensions are indeed in centimeters, or if there's any additional information to assist in providing a correct answer?