Explanation:
The volume of a cone is given by the formula:
V = (1/3)πr^2h
where r is the radius of the base and h is the height of the cone.
In this case, the cone has a height of 14 cm and a base radius of 4/2 cm, which is equal to 2 cm. Therefore, the volume of the entire cone is:
V = (1/3)π(2 cm)^2(14 cm) = (4/3)π(28 cm^3) = 37.333... cm^3
To find the volume of water that is exactly half the volume of the cone, we need to divide the volume of the cone by 2:
V_water = (1/2)V = (1/2)(37.333...) cm^3 = 18.666... cm^3
To calculate the height of the water in the cone, we can use the formula:
V_water = (1/3)πr^2h
where h is the height of the water.
We know the volume of water (18.666... cm^3) and the radius of the base (2 cm), so we can rearrange the formula to solve for h:
h = 3V_water / (πr^2) = 3(18.666...) / (π(2 cm)^2) ≈ 2.366 cm
Therefore, the height of the water in the cone is approximately 2.366 cm.