find the volume of cone with the radius 4 and hight 12

The volume \( V \) of a cone can be calculated using the formula:

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

where:

• \( r \) is the radius of the base of the cone,
• \( h \) is the height of the cone.

Given:

• Radius \( r = 4 \)
• Height \( h = 12 \)

Substituting the values into the formula:

\[ V = \frac{1}{3} \pi (4)^2 (12) \]

Calculating \( (4)^2 \):

\[ (4)^2 = 16 \]

Now substituting back:

\[ V = \frac{1}{3} \pi (16)(12) \]

Calculating \( 16 \times 12 \):

\[ 16 \times 12 = 192 \]

Now substituting this value in:

\[ V = \frac{1}{3} \pi (192) \]

Calculating \( \frac{192}{3} \):

\[ \frac{192}{3} = 64 \]

Thus, the volume \( V \) simplifies to:

\[ V = 64\pi \]

Therefore, the volume of the cone is

\[ \boxed{64\pi} \]

If you want a numerical approximation, you can use \( \pi \approx 3.14 \):

\[ V \approx 64 \times 3.14 \approx 200.96 \]

So the volume is approximately \( 200.96 \) cubic units.

The volume \( V \) of a cylinder can be calculated using the formula:

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

where:

• \( r \) is the radius of the base of the cylinder,
• \( h \) is the height of the cylinder.

Given:

• Radius \( r = 5 \)
• Height \( h = 15 \)

Substituting the values into the formula:

\[ V = \pi (5)^2 (15) \]

Calculating \( (5)^2 \):

\[ (5)^2 = 25 \]

Now substituting this value in:

\[ V = \pi (25)(15) \]

Calculating \( 25 \times 15 \):

\[ 25 \times 15 = 375 \]

Thus, the volume \( V \) simplifies to:

\[ V = 375\pi \]

Therefore, the volume of the cylinder is

\[ \boxed{375\pi} \]

If you want a numerical approximation, you can use \( \pi \approx 3.14 \):

\[ V \approx 375 \times 3.14 \approx 1177.5 \]

So the volume is approximately \( 1177.5 \) cubic units.

No problem! Let's calculate the volume of a cone with a radius of 5 and a height of 15.

The volume \( V \) of a cone can be calculated using the formula:

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

where:

• \( r \) is the radius of the base of the cone,
• \( h \) is the height of the cone.

Given:

• Radius \( r = 5 \)
• Height \( h = 15 \)

Substituting the values into the formula:

\[ V = \frac{1}{3} \pi (5)^2 (15) \]

Calculating \( (5)^2 \):

\[ (5)^2 = 25 \]

Now substituting this value back into the formula:

\[ V = \frac{1}{3} \pi (25)(15) \]

Next, calculate \( 25 \times 15 \):

\[ 25 \times 15 = 375 \]

Now substituting this value in:

\[ V = \frac{1}{3} \pi (375) \]

Calculating \( \frac{375}{3} \):

\[ \frac{375}{3} = 125 \]

Thus, the volume \( V \) simplifies to:

\[ V = 125\pi \]

Therefore, the volume of the cone is

\[ \boxed{125\pi} \]

If you want a numerical approximation, using \( \pi \approx 3.14 \):

\[ V \approx 125 \times 3.14 \approx 392.5 \]

So the volume is approximately \( 392.5 \) cubic units.

The volume \( V \) of a sphere can be calculated using the formula:

\[ V = \frac{4}{3} \pi r^3 \]

where:

• \( r \) is the radius of the sphere.

Given:

• Radius \( r = 5 \)

Substituting the value into the formula:

\[ V = \frac{4}{3} \pi (5)^3 \]

Calculating \( (5)^3 \):

\[ (5)^3 = 125 \]

Now substituting this value back into the formula:

\[ V = \frac{4}{3} \pi (125) \]

Calculating \( \frac{4 \times 125}{3} \):

\[ V = \frac{500}{3} \pi \]

Thus, the volume \( V \) simplifies to:

\[ V = \frac{500}{3} \pi \]

Therefore, the volume of the sphere is

\[ \boxed{\frac{500}{3} \pi} \]

If you'd like a numerical approximation, using \( \pi \approx 3.14 \):

\[ V \approx \frac{500}{3} \times 3.14 \approx 523.33 \]

So the volume is approximately \( 523.33 \) cubic units.

To find the volume \( V \) of a sphere, you can use the formula:

\[ V = \frac{4}{3} \pi r^3 \]

where:

• \( r \) is the radius of the sphere.

Given:

• Radius \( r = 4 \)

Substituting the value into the formula:

\[ V = \frac{4}{3} \pi (4)^3 \]

Calculating \( (4)^3 \):

\[ (4)^3 = 64 \]

Now substituting this value back into the formula:

\[ V = \frac{4}{3} \pi (64) \]

Calculating \( \frac{4 \times 64}{3} \):

\[ V = \frac{256}{3} \pi \]

Thus, the volume \( V \) simplifies to:

\[ V = \frac{256}{3} \pi \]

Therefore, the volume of the sphere is

\[ \boxed{\frac{256}{3} \pi} \]

If you would like a numerical approximation using \( \pi \approx 3.14 \):

\[ V \approx \frac{256}{3} \times 3.14 \approx 268.67 \]

So the volume is approximately \( 268.67 \) cubic units.