Question
Find the volume of the soda cans:
old new
radius 3160cm radius 2.720cm
124in 1.07in
height height
11.316cm 15.275cm
4.45in 6.01in
What common mistakes could you make when finding the volume of a cylinder using the formula: V = r2h?
old new
radius 3160cm radius 2.720cm
124in 1.07in
height height
11.316cm 15.275cm
4.45in 6.01in
What common mistakes could you make when finding the volume of a cylinder using the formula: V = r2h?
Answers
GPT-4o mini
To find the volume of a cylinder, we use the formula:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is approximately 3.14159.
Here are the steps to find the volume of both the old and new soda cans, including potential common mistakes.
### Old Can:
1. **Convert the radius and height into the same unit:**
- The radius is given as 3160 cm (assuming this was a typo and should be 3.16 cm).
- The height is given as 11.316 cm.
2. **Calculate the volume:**
\[
V = \pi r^2 h = \pi (3.16)^2 (11.316)
\]
3. **Calculate \( r^2 \):**
\[
r^2 = 3.16^2 \approx 10.016
\]
4. **Calculate the volume:**
\[
V \approx \pi \times 10.016 \times 11.316 \approx 3.14159 \times 10.016 \times 11.316 \approx 357.34 \, \text{cm}^3
\]
### New Can:
1. **Use the radius and height in the same units:**
- The radius is 2.720 cm.
- The height is 15.275 cm.
2. **Calculate the volume:**
\[
V = \pi r^2 h = \pi (2.720)^2 (15.275)
\]
3. **Calculate \( r^2 \):**
\[
r^2 = 2.720^2 \approx 7.398
\]
4. **Calculate the volume:**
\[
V \approx \pi \times 7.398 \times 15.275 \approx 3.14159 \times 7.398 \times 15.275 \approx 356.14 \, \text{cm}^3
\]
### Common mistakes when finding the volume of a cylinder:
1. **Incorrectly squaring the radius:** Forgetting to square the radius (\( r^2 \)) correctly can lead to incorrect volume calculations.
2. **Using inconsistent units:** Using different units for radius and height (e.g., mixing inches and centimeters) without conversion can result in incorrect volume.
3. **Neglecting π or approximating incorrectly:** Forgetting to include π or using an incorrect approximation for π can lead to significant errors.
4. **Misplacing decimal points:** This is a common error, especially when dealing with measurements that have several digits.
5. **Not converting all measurements when necessary:** Sometimes measurements may need conversion before applying the formula.
Double-checking calculations and ensuring unit consistency are key to avoiding these errors!
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is approximately 3.14159.
Here are the steps to find the volume of both the old and new soda cans, including potential common mistakes.
### Old Can:
1. **Convert the radius and height into the same unit:**
- The radius is given as 3160 cm (assuming this was a typo and should be 3.16 cm).
- The height is given as 11.316 cm.
2. **Calculate the volume:**
\[
V = \pi r^2 h = \pi (3.16)^2 (11.316)
\]
3. **Calculate \( r^2 \):**
\[
r^2 = 3.16^2 \approx 10.016
\]
4. **Calculate the volume:**
\[
V \approx \pi \times 10.016 \times 11.316 \approx 3.14159 \times 10.016 \times 11.316 \approx 357.34 \, \text{cm}^3
\]
### New Can:
1. **Use the radius and height in the same units:**
- The radius is 2.720 cm.
- The height is 15.275 cm.
2. **Calculate the volume:**
\[
V = \pi r^2 h = \pi (2.720)^2 (15.275)
\]
3. **Calculate \( r^2 \):**
\[
r^2 = 2.720^2 \approx 7.398
\]
4. **Calculate the volume:**
\[
V \approx \pi \times 7.398 \times 15.275 \approx 3.14159 \times 7.398 \times 15.275 \approx 356.14 \, \text{cm}^3
\]
### Common mistakes when finding the volume of a cylinder:
1. **Incorrectly squaring the radius:** Forgetting to square the radius (\( r^2 \)) correctly can lead to incorrect volume calculations.
2. **Using inconsistent units:** Using different units for radius and height (e.g., mixing inches and centimeters) without conversion can result in incorrect volume.
3. **Neglecting π or approximating incorrectly:** Forgetting to include π or using an incorrect approximation for π can lead to significant errors.
4. **Misplacing decimal points:** This is a common error, especially when dealing with measurements that have several digits.
5. **Not converting all measurements when necessary:** Sometimes measurements may need conversion before applying the formula.
Double-checking calculations and ensuring unit consistency are key to avoiding these errors!