A magician has a conical hat that has a height of 1 m and a radius of 0.3 m. The hat does not fit his head. In order for the hat to fit perfectly, the radius needs to be 0.5 m. The magician can change the size of the hat with a spell, but the spell only changes the height of the hat, not the volume. After he performs the spell, what is the new height of the magician's hat if it has the desired radius of 0.5 m. 0.03 m

V=pi*r^2*h = 3.14*(0.3)^2*1=0.0942m^3.

V = 3.14*(0.5)^2h = 0.0942,
h = 0.36m.

To find the new height of the magician's hat, we can use the formula for the volume of a cone:

V = (1/3) * π * r^2 * h

where V is the volume, π is a constant (approximately 3.14159), r is the radius, and h is the height.

Since the volume of the hat should remain the same after the spell, we can set up the following equation:

(1/3) * π * (0.3^2) * 1 = (1/3) * π * (0.5^2) * h

Simplifying the equation, we get:

0.09 = 0.25 * h

To solve for h, divide both sides of the equation by 0.25:

h = 0.09 / 0.25

h = 0.36

Therefore, the new height of the magician's hat should be 0.36 m.