The volume of a cone is 27 cm^3. What is the volume of a cylinder that shares the same radius and height as the cone? Answer correctly

Answer 1

The volume \( V \) of a cone is given by the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

where \( r \) is the radius and \( h \) is the height of the cone. Given that the volume of the cone is \( 27 , \text{cm}^3 \), we can write:

\[ \frac{1}{3} \pi r^2 h = 27 \]

Now, the volume \( V \) of a cylinder with the same radius and height is given by the formula:

\[ V = \pi r^2 h \]

To find the volume of the cylinder, we can relate it to the volume of the cone. Since the volume of a cylinder is three times the volume of a cone with the same base and height, we have:

\[ V_{\text{cylinder}} = 3 \times V_{\text{cone}} \]

Substituting the volume of the cone:

\[ V_{\text{cylinder}} = 3 \times 27 = 81 , \text{cm}^3 \]

Thus, the volume of the cylinder is:

\[ \boxed{81 , \text{cm}^3} \]

Answer 2

give me the formula/question to answer this

Answer 3

To find the volume of a cylinder given the volume of a cone that shares the same radius and height, you can start with the following steps and related formulas:

1. Volume of a Cone: The formula for the volume of a cone is: \[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.

2. Volume of a Cylinder: The formula for the volume of a cylinder is: \[ V_{\text{cylinder}} = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.

3. Relationship between Cone and Cylinder Volumes: Given that the cylinder has the same radius and height as the cone, we can relate the two volumes: \[ V_{\text{cylinder}} = 3 \times V_{\text{cone}} \]

Example Question:

If the volume of a cone is \( 27 , \text{cm}^3 \), what is the volume of a cylinder that shares the same radius and height as the cone?

Steps to Solve:

1. Use the volume of the cone to find the volume of the cylinder by multiplying: \[ V_{\text{cylinder}} = 3 \times V_{\text{cone}} \]

2. Substitute the given volume of the cone: \[ V_{\text{cylinder}} = 3 \times 27 \]

3. Calculate: \[ V_{\text{cylinder}} = 81 , \text{cm}^3 \]

Final Answer:

The volume of the cylinder is \( \boxed{81 , \text{cm}^3} \).

Answer 4

pick one of these answers
1.5x + 0.5
1.5
𝑥

+

0.5
1.5 x plus 0.5

6x + 2
6
𝑥

+

2
6 x plus 2

x + 13
𝑥

+

1
3
x plus Start Fraction 1 over 3 End Fraction

9x + 3

Answer 5

It seems like you're asking to choose one of the expressions provided, but you haven't given any context or criteria for selection. However, to assist you, I'll simply choose one of the expressions at random:

Selected Answer: \( 6x + 2 \)

If you have a specific guideline or context for your request, please let me know!