Question
Cynthia used a cylinder-shaped container to catch rainwater. The dimensions of the container are show below. The hiegth is 12cm, The width is 8 cm
Which measurement is closest to the volume of the container in cubic centimeter?
Responses
A 574.89 cm³574.89 cm³
B 603.19 cm³603.19 cm³
C 1,357.17 cm³1,357.17 cm³
D 2,412.74 cm³
Which measurement is closest to the volume of the container in cubic centimeter?
Responses
A 574.89 cm³574.89 cm³
B 603.19 cm³603.19 cm³
C 1,357.17 cm³1,357.17 cm³
D 2,412.74 cm³
Answers
GPT-4o mini
To find the volume of a cylinder, you use the formula:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given the width of the cylinder is 8 cm, the radius \( r \) would be half of the width:
\[ r = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm} \]
The height \( h \) is given as 12 cm.
Now we can substitute the values into the volume formula:
\[ V = \pi (4 \, \text{cm})^2 (12 \, \text{cm}) \]
\[ V = \pi (16 \, \text{cm}^2) (12 \, \text{cm}) \]
\[ V = 192\pi \, \text{cm}^3 \]
To approximate this volume, use \( \pi \approx 3.14 \):
\[ V \approx 192 \times 3.14 \]
\[ V \approx 602.88 \, \text{cm}^3 \]
Looking at the given options, the closest volume to our calculation is:
**B: 603.19 cm³**
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given the width of the cylinder is 8 cm, the radius \( r \) would be half of the width:
\[ r = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm} \]
The height \( h \) is given as 12 cm.
Now we can substitute the values into the volume formula:
\[ V = \pi (4 \, \text{cm})^2 (12 \, \text{cm}) \]
\[ V = \pi (16 \, \text{cm}^2) (12 \, \text{cm}) \]
\[ V = 192\pi \, \text{cm}^3 \]
To approximate this volume, use \( \pi \approx 3.14 \):
\[ V \approx 192 \times 3.14 \]
\[ V \approx 602.88 \, \text{cm}^3 \]
Looking at the given options, the closest volume to our calculation is:
**B: 603.19 cm³**