Look at the com below the line and through the middle is 5 feet. The outside angle line is 13 feet. How many feet long is the radius of the cone

Answer 1

To solve this problem, we need to clarify what dimensions are given and how they relate to a cone's geometry.

We have:

1. The height from the bottom to the middle (which is likely the height of the cone) is 5 feet.
2. The slant height (the outer angled line) of the cone is 13 feet.

In a right circular cone, the relationship between the radius (\( r \)), height (\( h \)), and slant height (\( l \)) can be expressed using the Pythagorean theorem:

\[ l^2 = r^2 + h^2 \]

Where:

• \( l \) is the slant height,
• \( r \) is the radius,
• \( h \) is the height.

Given:

• \( h = 5 \) feet,
• \( l = 13 \) feet.

We can substitute these values into the equation:

\[ 13^2 = r^2 + 5^2 \]

Calculating the squares:

\[ 169 = r^2 + 25 \]

Now, solve for \( r^2 \):

\[ r^2 = 169 - 25 \] \[ r^2 = 144 \]

Taking the square root to solve for \( r \):

\[ r = \sqrt{144} \] \[ r = 12 \]

Thus, the radius of the cone is 12 feet.

Answer 2

Look at the cone the middle line is 21 feet by bases 20 feet how many feet long is the slant height of a cone?

Answer 3

To find the slant height of the cone, we can again use the Pythagorean theorem. The height \( (h) \) of the cone and the radius \( (r) \) of the base are related to the slant height \( (l) \).

Given:

• The height of the cone is \( h = 21 \) feet.
• The diameter of the base is \( 20 \) feet, which means the radius \( r \) is:

\[ r = \frac{\text{diameter}}{2} = \frac{20}{2} = 10 \text{ feet} \]

Using the Pythagorean theorem, we have:

\[ l^2 = r^2 + h^2 \]

Substituting the known values:

\[ l^2 = 10^2 + 21^2 \]

Calculating the squares:

\[ l^2 = 100 + 441 \]

Adding these together:

\[ l^2 = 541 \]

Now, take the square root to find \( l \):

\[ l = \sqrt{541} \]

Calculating the square root:

\[ l \approx 23.26 \text{ feet} \]

Thus, the slant height of the cone is approximately 23.26 feet.

Answer 4

Look at the cone the middle up-and-down line is 21 feet. The middle to the outer side is 20 feet. What is the length of the slant height of the cone?

Answer 5

From your description, it seems like:

• The vertical height of the cone \( (h) \) is 21 feet.
• The distance from the center of the base to a point on the edge of the base (which is the radius \( r \)) is 20 feet.

Given these values:

• \( h = 21 \) feet (height)
• \( r = 20 \) feet (radius)

To find the slant height \( (l) \) of the cone, we can use the Pythagorean theorem, which states:

\[ l^2 = r^2 + h^2 \]

Substituting the known values:

\[ l^2 = 20^2 + 21^2 \]

Calculating the squares:

\[ l^2 = 400 + 441 \]

Adding these together:

\[ l^2 = 841 \]

Now, take the square root to find \( l \):

\[ l = \sqrt{841} \]

Calculating the square root:

\[ l = 29 \text{ feet} \]

Thus, the length of the slant height of the cone is 29 feet.

Answer 6

Look at the square pyramid the base is 3MI The slant is fiveM what is the middle line the height?

Answer 7

To find the height of a square pyramid given the length of the base (side of the square) and the slant height, we can use the Pythagorean theorem.

1. Base half-length (\( r \)): Since the base is a square with a side length of 3 meters (3 m), the distance from the center of the base to the midpoint of one side (which we'll denote as \( r \)) is:

   \[ r = \frac{\text{side length}}{2} = \frac{3 , \text{m}}{2} = 1.5 , \text{m} \]

2. Slant height (\( l \)): The slant height is given as 5 m.

Now, we can relate these values using the Pythagorean theorem:

\[ l^2 = h^2 + r^2 \]

Where:

• \( l \) is the slant height,
• \( h \) is the height of the pyramid,
• \( r \) is the distance from the center of the base to the midpoint of one side.

Substituting the known values:

\[ 5^2 = h^2 + (1.5)^2 \]

Calculating the squares:

\[ 25 = h^2 + 2.25 \]

Now, isolate \( h^2 \):

\[ h^2 = 25 - 2.25 \] \[ h^2 = 22.75 \]

Taking the square root to find \( h \):

\[ h = \sqrt{22.75} \approx 4.77 \text{ m} \]

Therefore, the height of the square pyramid is approximately 4.77 meters.

Answer 8

Look at the square pyramid the baseline is 3MI the slant is 5MI what is the height of the square pyramid?

Answer 9

To find the height of a square pyramid given the side length of the base and the slant height, we will use the Pythagorean theorem.

1. Base side length (\( s \)): The side length of the base is given as 3 meters (3 m).
2. Slant height (\( l \)): The slant height is given as 5 meters (5 m).

Steps to Calculate Height

First, we need to find the distance from the center of the base to the midpoint of one side of the base (this is the radius \( r \)):

• Since the base is a square with a side length of 3 m:

\[ r = \frac{s}{2} = \frac{3 , \text{m}}{2} = 1.5 , \text{m} \]

Now we can use the Pythagorean theorem to relate the height (\( h \)), the radius (\( r \)), and the slant height (\( l \)):

\[ l^2 = h^2 + r^2 \]

Substituting the known values:

\[ 5^2 = h^2 + (1.5)^2 \]

Calculating the squares:

\[ 25 = h^2 + 2.25 \]

Now, isolate \( h^2 \):

\[ h^2 = 25 - 2.25 \] \[ h^2 = 22.75 \]

Taking the square root to find \( h \):

\[ h = \sqrt{22.75} \approx 4.77 , \text{m} \]

Conclusion

Therefore, the height of the square pyramid is approximately 4.77 meters.

Answer 10

That’s not the correct answer

Answer 11

Let's go through the problem step by step once again to ensure we get the correct answer for the height of the square pyramid.

Given:

1. Side length of the base (\( s \)) = 3 meters (3 m)
2. Slant height (\( l \)) = 5 meters (5 m)

Goal:

Find the vertical height (\( h \)) of the pyramid.

Steps:

1. Calculate the distance from the center of the base to the midpoint of one side (the radius): \[ r = \frac{s}{2} = \frac{3}{2} = 1.5 , \text{meters} \]

2. Use the Pythagorean theorem to relate the slant height, height, and the radius: \[ l^2 = h^2 + r^2 \] Substituting the known values: \[ 5^2 = h^2 + (1.5)^2 \]

3. Calculate: \[ 25 = h^2 + 2.25 \] \[ h^2 = 25 - 2.25 \] \[ h^2 = 22.75 \] \[ h = \sqrt{22.75} \approx 4.77 , \text{meters} \]

Conclusion:

The calculations are indeed consistent with the use of the Pythagorean theorem, and the height should be approximately 4.77 meters.

If there are any specific aspects of the problem or conditions that might lead to a different answer, please clarify, and I'll be happy to look into it further!