what is the length of the cone (1 point) 6, 4, 2

Answer 1

To determine the length of a cone given the parameters (6, 4, 2), we need to clarify what these numbers represent. If we assume they refer to the dimensions of the cone, here's how they might break down:

• Height (h): 6
• Radius (r): 4
• Slant Height (l): 2

However, in this scenario, the slant height (l) cannot be less than the radius (r) or height (h). The slant height of a right circular cone can be calculated using the Pythagorean theorem as follows:

\[ l = \sqrt{r^2 + h^2} \]

If we put in the values for radius (4) and height (6):

\[ l = \sqrt{4^2 + 6^2} = \sqrt{16 + 36} = \sqrt{52} \approx 7.21 \]

So, if you're looking for the slant height based on height and radius, it would be approximately 7.21.

If you meant something else by "length of the cone," please provide additional clarification!

Answer 2

6cm, 4cm, 2cm

Answer 3

To find the length of a cone with dimensions of height (h) = 6 cm, radius (r) = 4 cm, and slant height (l) = 2 cm, we need to clarify what each dimension represents. Based on your input, it seems you are providing three measurements.

1. Height (h): 6 cm
2. Radius (r): 4 cm
3. Slant Height (l): This cannot be 2 cm in a typical situation, since the slant height must be greater than the height of the cone in a right circular cone configuration.

Using the Pythagorean theorem to calculate the slant height, we have:

\[ l = \sqrt{r^2 + h^2} \] Substituting in the values:

• Radius (r) = 4 cm,
• Height (h) = 6 cm,

The slant height calculation is:

\[ l = \sqrt{4^2 + 6^2} = \sqrt{16 + 36} = \sqrt{52} \approx 7.21 , \text{cm} \]

If you are looking for a different calculation related to the cone or if the dimensions correspond to a specific configuration, please clarify your question!

Answer 4

cylinders and cones practice question 3

Answer 5

It seems like you're referring to a practice question related to cylinders and cones. While I don't have the specific question "Cylinders and Cones Practice Question 3," I can create a general practice problem related to these shapes. If you have the specific question, please share it, and I'll do my best to help you!

Sample Practice Question:

Question:

A cylinder has a radius of 5 cm and a height of 10 cm. A cone with the same radius and height is placed on top of the cylinder.

1. Calculate the volume of the cylinder.
2. Calculate the volume of the cone.
3. What is the total volume of the cylinder and the cone combined?

Answers:

1. Volume of the Cylinder (V_cylinder): The volume \( V \) of a cylinder is calculated using the formula: \[ V = \pi r^2 h \] Substituting in the values:

   • \( r = 5 , \text{cm} \)
   • \( h = 10 , \text{cm} \)

   \[ V_{cylinder} = \pi (5)^2 (10) = \pi (25) (10) = 250\pi \approx 785.40 \text{ cm}^3 \]

2. Volume of the Cone (V_cone): The volume \( V \) of a cone is calculated using the formula: \[ V = \frac{1}{3} \pi r^2 h \] Substituting in the same values:

   • \( r = 5 , \text{cm} \)
   • \( h = 10 , \text{cm} \)

   \[ V_{cone} = \frac{1}{3} \pi (5)^2 (10) = \frac{1}{3} \pi (25) (10) = \frac{250}{3} \pi \approx 261.80 \text{ cm}^3 \]

3. Total Volume: \[ V_{total} = V_{cylinder} + V_{cone} = 250\pi + \frac{250}{3}\pi \] To combine these, you can convert \(250\pi\) to have a common denominator: \[ V_{total} = \frac{750}{3}\pi + \frac{250}{3}\pi = \frac{1000}{3}\pi \approx 1047.20 \text{ cm}^3 \]

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If you have a specific practice question or need clarification on a particular topic related to cylinders and cones, please provide further details!

Answer 6

sorry vro im stupid

um the 6cm is inside the cone by a line on the left and the 4cm is on the right outside of the cone and the 2 cm is at the bottom of the cone. what is the length?

Answer 7

No need to apologize! Let's clarify the situation described with the cone and the given dimensions:

• 6 cm: This appears to be a vertical line representing the height of the cone (from the vertex of the cone to the base).
• 4 cm: This is likely the radius of the base of the cone.
• 2 cm: This might represent a distance that we need to find, possibly related to the slant height or the overall length when using these dimensions.

To find the slant height (l) of the cone, which is the length of a line from the base's edge to the apex (tip) of the cone, we can use the Pythagorean theorem.

Given:

• Height (h) = 6 cm
• Radius (r) = 4 cm

To find the slant height (l):

Using the Pythagorean theorem: \[ l = \sqrt{h^2 + r^2} \] Substituting the values: \[ l = \sqrt{(6 \text{ cm})^2 + (4 \text{ cm})^2} \] \[ l = \sqrt{36 + 16} \] \[ l = \sqrt{52} \] \[ l \approx 7.21 \text{ cm} \]

Summary:

• The slant height of the cone is approximately 7.21 cm.

If the "2 cm" dimension represents something specific (like a part of the cone or another measurement), please let me know! I hope this helps!

Answer 8

the 2cm is at the bottom inside the cone

Answer 9

Thank you for clarifying! If the 2 cm represents a segment at the bottom inside the cone, it appears that we are dealing with a cone that has a height of 6 cm, a radius of 4 cm, and an interior measurement of 2 cm possibly showing some separation inside the cone.

Based on your description, I assume that the 2 cm might indicate a segment from the apex of the cone to a point 2 cm above the base of the cone, leaving the remaining height of the cone to be 4 cm (since the total height is 6 cm).

Let's summarize:

• Total height of the cone (h): 6 cm
• Height above the base (inside the cone): 2 cm
• Radius of the base (r): 4 cm

To find out the length of the line (presumably you want to confirm the slant height or are looking for something else), we can consider this:

1. Remaining height above the 2cm segment:

   • Remaining height: \( \text{Total height} - \text{Height above base} = 6 \text{ cm} - 2 \text{ cm} = 4 \text{ cm} \)

2. To determine the slant height (l):

   • If you want the length of the slant height for the overall cone, we already calculated it as approximately 7.21 cm.
   • If you're looking for something different, such as the distance corresponding to just that 2 cm inside the cone, please provide more specifics.

If you're looking for the distance from the apex to the point where the cone is at 2 cm above the base:

Using the Pythagorean theorem again with the remaining height (4 cm) and the radius (4 cm) from the apex to the base:

Assuming that 2 cm is just a horizontal line drawn inside, the distance from the tip to that line can be calculated as:

• The overall height of the cone from apex to base is 6 cm.
• So, the slant height to the base was calculated as \( l = \sqrt{h^2 + r^2} \) where \( h = 6 \) and \( r = 4 \).

Please clarify if this aligns with your scenario and what specific distances or lengths you want to calculate!

Answer 10

7.21 isnt correct

Answer 11

I apologize for the confusion earlier! Let's clarify the matter and recalculate based on your description of the cone.

Given:

• Height of the cone (h): 6 cm (from vertex to the base)
• Radius of the base (r): 4 cm
• An internal height (measured inside from the vertex downward): 2 cm

Understanding the Dimensions:

1. The vertical height of the entire cone is 6 cm.
2. There is a line representing 2 cm measured from the vertex downward, which implies that the remaining height to the base is \(6 , \text{cm} - 2 , \text{cm} = 4 , \text{cm}\).
3. The radius at the base of the cone stays 4 cm.

Finding the Slant Height:

The slant height (l) refers to the length of the line from the base edge to the apex (tip) of the cone. To find this, we can use the full height of the cone (6 cm) and the radius (4 cm):

Using the Pythagorean theorem:

\[ l = \sqrt{r^2 + h^2} \]

Substituting in the values:

• \( r = 4 , \text{cm} \)
• \( h = 6 , \text{cm} \)

\[ l = \sqrt{(4 , \text{cm})^2 + (6 , \text{cm})^2} \] \[ l = \sqrt{16 + 36} \] \[ l = \sqrt{52} \] \[ l = 2\sqrt{13} \approx 7.21 , \text{cm} \]

Clarification of Measurements:

Since you're indicating there's a measurement of 2 cm internally:

If you're seeking the slant height up to the point where that 2 cm line is measured, we may need some adjustments.

However, given your description:

• If the 2 cm is a specific vertical line inside and does not affect the radius or the total cone's geometry, the calculated slant height would still be right, as you go from the apex (the tip) to the outer edge at the base.

Conclusion:

If 7.21 cm is still not aligning with what you're looking for, it might be useful to clarify what you're specifically measuring or if there's a certain angle/geometry you're aiming to assess based on missing information related to your intended measurement. Please specify further, and I'll gladly assist!