There is a cone whose Height is 12 and length is 10. What is the radius of the cone? (1 point)
12
8
10
4
We can use the formula for the volume of a cone to solve for the radius. The formula is V = (1/3)πr^2h, where V is the volume, π is a mathematical constant (approximately equal to 3.14159), r is the radius, and h is the height.
Plugging in the given values, we can solve for the radius:
10 = (1/3)πr^2(12)
Dividing both sides of the equation by (1/3) and (12), we get:
10 / ((1/3)(12)) = πr^2
Multiplying both sides by ((1/3)(12)), we get:
10 = (4π/3)r^2
Dividing both sides by (4π/3), we get:
(10 / (4π/3)) = r^2
Simplifying the right side, we get:
(10 * 3) / (4π) = r^2
30 / (4π) = r^2
Dividing both sides by π, we get:
30 / (4π^2) = r^2
Taking the square root of both sides, we get:
√(30 / (4π^2)) = r
Simplifying the right side, we get:
√(30 / (4π^2)) ≈ r
Approximately:
r ≈ 1.91
So, the radius of the cone is approximately 1.91.