Question
Two cans of vegetables were measured. Can A is 10 cm in diameter and has a height of 10.5 cm. Can B has a height of 11cm and a diameter of 7.5cm. Which can has the greater volume?
can A
can B
the two cans have equal volumes
more information is needed to solve the problem
can A
can B
the two cans have equal volumes
more information is needed to solve the problem
Answers
GPT-4o mini
To determine which can has a greater volume, we can use the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height of the cylinder.
**For Can A:**
- Diameter = 10 cm, so the radius \( r_A = \frac{10}{2} = 5 \) cm
- Height \( h_A = 10.5 \) cm
Calculating the volume:
\[
V_A = \pi (5^2)(10.5) = \pi (25)(10.5) = \pi (262.5) \approx 825.34 \text{ cm}^3
\]
**For Can B:**
- Diameter = 7.5 cm, so the radius \( r_B = \frac{7.5}{2} = 3.75 \) cm
- Height \( h_B = 11 \) cm
Calculating the volume:
\[
V_B = \pi (3.75^2)(11) = \pi (14.0625)(11) = \pi (154.6875) \approx 486.87 \text{ cm}^3
\]
**Comparison:**
- Volume of Can A: \( \approx 825.34 \text{ cm}^3 \)
- Volume of Can B: \( \approx 486.87 \text{ cm}^3 \)
Therefore, **Can A** has the greater volume.
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height of the cylinder.
**For Can A:**
- Diameter = 10 cm, so the radius \( r_A = \frac{10}{2} = 5 \) cm
- Height \( h_A = 10.5 \) cm
Calculating the volume:
\[
V_A = \pi (5^2)(10.5) = \pi (25)(10.5) = \pi (262.5) \approx 825.34 \text{ cm}^3
\]
**For Can B:**
- Diameter = 7.5 cm, so the radius \( r_B = \frac{7.5}{2} = 3.75 \) cm
- Height \( h_B = 11 \) cm
Calculating the volume:
\[
V_B = \pi (3.75^2)(11) = \pi (14.0625)(11) = \pi (154.6875) \approx 486.87 \text{ cm}^3
\]
**Comparison:**
- Volume of Can A: \( \approx 825.34 \text{ cm}^3 \)
- Volume of Can B: \( \approx 486.87 \text{ cm}^3 \)
Therefore, **Can A** has the greater volume.