What is the volume of a cylinder with a radius of 5 and a height of 3? What is the volume of a cylinder with a diameter of 10 and a height of 25? Which of the following is NOT equa... What is the volume of a cylinder with a radius of 5 and a height of 3? What is the volume of a cylinder with a diameter of 10 and a height of 25? Which of the following is NOT equal to the others? How many quarts are equivalent to 8 gallons? What is the volume of a cylinder with a diameter of 6 and a height of 10? A cylinder has a base area of 25π unit². If its volume is 250π unit³, what is its height? Which of the following units is NOT used to measure volume? The volume of a cylinder is 250π cm³, and its height is 10 cm. What is its radius? Which of the two containers can hold more water? If the height of the pyramid to your right is 14, what is its volume?
Understand the Problem
The questions consist of various mathematical problems related to geometry and volume calculations, focusing on cylinders, conversions between units, and determining the volumes of different shapes.
Answer
- Question 11: $75\pi$ - Question 12: $625\pi$
Answer for screen readers
- Question 11: $75\pi$ (Option D)
- Question 12: $625\pi$ (Option B)
Steps to Solve
- Identify the volume formula for a cylinder
The volume $V$ of a cylinder can be calculated using the formula:
$$ V = \pi r^2 h $$
where $r$ is the radius and $h$ is the height.
- Calculate the volume for the first question
For question 11:
- Given the radius $r = 5$ and height $h = 3$, substitute these values into the volume formula:
$$ V = \pi (5)^2 (3) $$
This simplifies to:
$$ V = \pi \cdot 25 \cdot 3 = 75\pi $$
- Identify the correct answer
The answer to question 11 is $75\pi$. Therefore, the correct option is D.
- Calculate the volume for the second question
For question 12:
- The diameter is given as 10, so the radius $r$ is $10/2 = 5$, and the height $h = 25$. Substitute these values into the volume formula:
$$ V = \pi (5)^2 (25) $$
This simplifies to:
$$ V = \pi \cdot 25 \cdot 25 = 625\pi $$
- Identify the correct answer for the second question
The answer to question 12 is $625\pi$. Therefore, the correct option is B.
- Question 11: $75\pi$ (Option D)
- Question 12: $625\pi$ (Option B)
More Information
The calculations for the volumes of cylinders rely on the relationship between the radius and height, emphasizing the significance of the radius being squared in the formula. The use of $\pi$ indicates the geometric nature of the problems.
Tips
- Ignoring the formula: Some may forget the correct volume formula for cylinders or misinterpret the radius.
- Using diameter instead of radius: Ensure to divide the diameter by 2 to find the radius before performing calculations.
AI-generated content may contain errors. Please verify critical information
