Use the z button in your calculations and round to the nearest whole
The formula for finding the volume of a cone is V = 1/3 vec A 2 . The volume of a cone is 262 and the height of the cone is 10 cm. What is the approximate radius of the cone?
The radius of the cone is approximately 8.7 cm (rounded to the nearest whole).
To find the approximate radius of the cone, we can rearrange the formula for the volume of a cone and solve for the radius.
The formula for the volume of a cone is:
V = (1/3) * π * r^2 * h
Where:
V is the volume of the cone,
r is the radius of the cone, and
h is the height of the cone.
Given:
V = 262 (volume)
h = 10 cm (height)
Now, let's rearrange the formula and solve for r:
262 = (1/3) * π * r^2 * 10
First, simplify the equation by multiplying both sides by 3 to eliminate the fraction:
3 * 262 = π * r^2 * 10
786 = 10π * r^2
Next, divide both sides by 10π:
786 / (10π) = r^2
78.6 / π = r^2
To find the value of r, we can calculate the square root of both sides:
√(78.6 / π) ≈ 5.00
Therefore, the approximate radius of the cone is 5 cm (rounded to the nearest whole).
To find the approximate radius of the cone, we'll use the given formula V = (1/3) * π * r^2 * h, where V is the volume, r is the radius, and h is the height.
In this case, we're given that the volume of the cone (V) is 262 and the height of the cone (h) is 10 cm.
Plugging the values into the formula, we get:
262 = (1/3) * π * r^2 * 10
To isolate the radius (r), we can rearrange the formula:
r^2 = (262 * 3) / (10 * π)
Simplifying the expression:
r^2 = 786 / (10 * π)
Now, let's solve for r:
r = √(786 / (10 * π))
Using the z button to round to the nearest whole:
r ≈ √(786 / (10 * 3.14))
r ≈ √(786 / 31.4)
r ≈ √(25.03)
r ≈ 5 cm
Therefore, the approximate radius of the cone is 5 cm.