To find the height of the cone, we can use the formula for the volume of a cone:

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

Where:

• $V$ is the volume of the cone (1,570 cubic inches),
• $r$ is the radius of the base (10 inches),
• $h$ is the height (which we are solving for),
• $\pi \approx 3.14$.

Step 1: Substitute known values into the formula

$1,570 = \frac{1}{3} \times 3.14 \times 10^2 \times h$ $1,570 = \frac{1}{3} \times 3.14 \times 100 \times h$ $1,570 = 104.67 \times h$

Step 2: Solve for $h$

$h = \frac{1,570}{104.67} \approx 15$

So, the height of the cone is approximately 15 inches.

Would you like further explanation or have any questions?

Here are some related questions you might find interesting:

1. How does the volume change if the radius is doubled?
2. What happens to the height if the volume is halved?
3. Can we use the formula for volume of a cone to calculate the slant height?
4. How would the volume of the cone change if we used a different approximation for $\pi$?
5. What is the surface area of a cone with this radius and height?

Tip: Remember that the height of a cone is always perpendicular to the base, while the slant height is the distance from the top of the cone to the edge of the base along the cone’s surface.