An oblique cone shows a base radius of 9 inches. The perpendicular height is 5 inches from the apex to the base outside the cone. A right angle is formed outside the cone to the right. A dashed diagonal line connects the center of the circular base to the apex.

Question

what is the volume of the cone? Use 3.14 for pi

942 cubic inches

423.9 cubic inches

47.1 cubic inches

235.5 cubic inches

GPT-4o mini · Answer

To find the volume of a cone, you can use the formula:

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

where:

\( V \) is the volume,
\( r \) is the radius of the base,
\( h \) is the height.

In this case:

The base radius \( r = 9 \) inches,
The height \( h = 5 \) inches.

Now, plug in the values into the formula:

\[ V = \frac{1}{3} \times 3.14 \times (9^2) \times 5 \]

Calculate \( 9^2 \):

\[ 9^2 = 81 \]

Now plug that value back into the equation:

\[ V = \frac{1}{3} \times 3.14 \times 81 \times 5 \]

Calculate \( 81 \times 5 \):

\[ 81 \times 5 = 405 \]

Now, you can substitute that back in:

\[ V = \frac{1}{3} \times 3.14 \times 405 \]

Calculate \( \frac{1}{3} \times 405 \):

\[ \frac{405}{3} = 135 \]

Now multiply \( 135 \) by \( 3.14 \):

\[ V = 135 \times 3.14 = 423.9 \]

Thus, the volume of the cone is:

\[ \boxed{423.9 \text{ cubic inches}} \]

adam · Answer

A right cone shows a base radius of 5 centimeters and a perpendicular height of 9 centimeters. A right angle is formed with the diameter and the height at the center of the circular base.

what is the volume of the cone in cubic centimeters? Use 3.14 for pi. Round your answer to the nearest tenth

__ cubic centimeters

GPT-4o mini · Answer

To find the volume of a right cone, you can use the formula:

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

where:

\( V \) is the volume,
\( r \) is the radius of the base,
\( h \) is the height.

In this case:

The base radius \( r = 5 \) centimeters,
The height \( h = 9 \) centimeters.

Now, substitute the values into the formula:

\[ V = \frac{1}{3} \times 3.14 \times (5^2) \times 9 \]

Calculate \( 5^2 \):

\[ 5^2 = 25 \]

Now substitute that value back into the equation:

\[ V = \frac{1}{3} \times 3.14 \times 25 \times 9 \]

Calculate \( 25 \times 9 \):

\[ 25 \times 9 = 225 \]

Now you can substitute that back in:

\[ V = \frac{1}{3} \times 3.14 \times 225 \]

Calculate \( \frac{1}{3} \times 225 \):

\[ \frac{225}{3} = 75 \]

Now multiply \( 75 \) by \( 3.14 \):

\[ V = 75 \times 3.14 = 235.5 \]

Rounding to the nearest tenth, the volume of the cone is:

\[ \boxed{235.5} \text{ cubic centimeters} \]

adam · Answer

A right cone shows a base diameter of 14 millimeters and a perpendicular height of 12 millimeters. A right angle is formed with the diameter and the height at the center of the circular base.

What is the volume, in cubic centimeters, of the cone? Use 3.14 for pi. Round your answer to the nearest hundredth.

__ cubic millimeters

GPT-4o mini · Answer

To find the volume of a right cone, you can use the formula:

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

Where:

\( V \) is the volume,
\( r \) is the radius of the base,
\( h \) is the height.

Given:

The base diameter is 14 millimeters, which means the radius \( r \) is half of the diameter:

\[ r = \frac{14}{2} = 7 \text{ mm} \]

The height \( h = 12 \) millimeters.

Now substitute the values into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times (7^2) \times 12 \]

Calculate \( 7^2 \):

\[ 7^2 = 49 \]

Now substitute that value back in:

\[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]

Calculate \( 49 \times 12 \):

\[ 49 \times 12 = 588 \]

Now substitute that back in:

\[ V = \frac{1}{3} \times 3.14 \times 588 \]

Calculate \( \frac{1}{3} \times 588 \):

\[ \frac{588}{3} = 196 \]

Now multiply \( 196 \) by \( 3.14 \):

\[ V = 196 \times 3.14 = 615.44 \]

Thus, the volume of the cone is:

\[ 615.44 \text{ cubic millimeters} \]

Finally, rounding to the nearest hundredth, the volume of the cone is:

\[ \boxed{615.44} \text{ cubic millimeters} \]

adam · Answer

Find the surface area of a sphere with a diameter of 40 inches. Leave your answer in terms of pi. The surface area is ___ in.^2

GPT-4o mini · Answer

To find the surface area of a sphere, you can use the formula:

\[ SA = 4 \pi r^2 \]

where \( SA \) is the surface area and \( r \) is the radius of the sphere.

Given that the diameter of the sphere is 40 inches, we can find the radius \( r \):

\[ r = \frac{\text{diameter}}{2} = \frac{40}{2} = 20 \text{ inches} \]

Now, substitute the radius into the surface area formula:

\[ SA = 4 \pi (20)^2 \]

Calculate \( (20)^2 \):

\[ (20)^2 = 400 \]

Now substitute that back into the equation:

\[ SA = 4 \pi \times 400 \]

Now calculate \( 4 \times 400 \):

\[ 4 \times 400 = 1600 \]

Thus, the surface area of the sphere is:

\[ SA = 1600\pi \]

So, the surface area is:

\[ \boxed{1600\pi} \text{ in}^2 \]

adam · Answer

Find the surface area of a sphere with a radius of 3.6 ft. Use 3.14 for pi. Round your answer to the nearest hundredth, if necessary The surface area is __ ft.^2

GPT-4o mini · Answer

To find the surface area of a sphere, you can use the formula:

\[ SA = 4 \pi r^2 \]

Given the radius \( r = 3.6 \) feet, you can substitute this value into the formula. First, calculate \( r^2 \):

\[ r^2 = (3.6)^2 = 12.96 \]

Now substitute \( r^2 \) back into the surface area formula:

\[ SA = 4 \times 3.14 \times 12.96 \]

Now perform the multiplication step-by-step:

Calculate \( 4 \times 3.14 \):

\[ 4 \times 3.14 = 12.56 \]

Now multiply this result by \( 12.96 \):

\[ SA = 12.56 \times 12.96 \]

Calculating that gives:

\[ SA \approx 162.7336 \]

Now, round the answer to the nearest hundredth:

\[ SA \approx 162.73 \]

Therefore, the surface area of the sphere is:

\[ \boxed{162.73} \text{ ft}^2 \]

adam · Answer

thats not correct

GPT-4o mini · Answer

Let's recalculate the surface area of a sphere with a radius of 3.6 ft using the correct formula and steps carefully.

The formula for the surface area \( SA \) of a sphere is:

\[ SA = 4 \pi r^2 \]

Given:

Radius \( r = 3.6 \) ft

Calculate \( r^2 \):

\[ r^2 = (3.6)^2 = 12.96 \]

Substitute \( r^2 \) into the surface area formula:

\[ SA = 4 \times 3.14 \times 12.96 \]

Calculate \( 4 \times 3.14 \):

\[ 4 \times 3.14 = 12.56 \]

Now multiply this by \( 12.96 \):

\[ SA = 12.56 \times 12.96 \]

Performing the multiplication:

\[ SA = 12.56 \times 12.96 \approx 162.7336 \]

Round the result to the nearest hundredth:

\[ SA \approx 162.73 , \text{ft}^2 \]

Hence, after recalculating, the correct surface area of the sphere is:

\[ \boxed{162.73} , \text{ft}^2 \]

If this still doesn't align with the expected answer, please let me know what the discrepancy may be.