Unclear if the area of the base is diameter or radius. Thank you.
The area of the base of a cylinder is 46 square inches and its height is 11 inches. A cone has the same area for its base and the same height. What is the cone's volume?
cylinder ... v = (base area) * (height)
cone ... v = (1/3) * (base area) * (height)
To find the volume of a cone, we first need to determine the radius of its base. In this particular problem, the area of the base of the cylinder is given as 46 square inches. However, it is unclear whether this measurement refers to the diameter or the radius.
If the area is given in terms of the diameter, we will need to convert it to the radius before proceeding with the calculations. The radius is half the diameter. So, if the area measurement is given as the diameter, we would need to divide it by 2 to obtain the radius.
Once we have the radius of the base, we can calculate the volume of the cone using the formula:
Volume of a cone = (1/3) * (π * r^2 * h)
where r is the radius of the base and h is the height.
Now, let's assume that the 46 square inches represents the area of the base as the radius. In this case, we can proceed with the calculations.
First, we need to find the radius of the base of the cylinder from the given area of 46 square inches. Since the area of a circle is given by the formula π * r^2, we can rearrange the formula to solve for the radius:
π * r^2 = 46
Dividing both sides by π:
r^2 = 46 / π
Taking the square root of both sides:
r ≈ √(46 / π)
Now that we have the radius of the base, we can calculate the volume of the cone by substituting the values into the formula:
Volume of a cone = (1/3) * (π * r^2 * h)
Where h is given as 11 inches:
Volume of the cone = (1/3) * (π * √(46 / π))^2 * 11
Simplifying the equation, we can plug these values into a calculator to find the actual volume.