A water level in a spherical bowl has a diameter of 30cm. If the horizontal diameter of the bowl is 10cm below the water level, calculate the radius of the bowl and the depth of the water in the bowl
there are two possible answers:
sketch a cross-section, and complete the right-angled triangle
let the radius be r
r^2 = 10^2 + 15^2
r = √325
depth of water = 10 + √325
= 18.303
or
Let the radius be r
R^2=5^2+15^2
R =√250
R =15.8
Depth of water = 5 + 15.8
= 20.8
To find the radius of the bowl, we can divide the diameter by 2.
Given:
Diameter of the bowl = 30 cm
Radius of the bowl = Diameter / 2
= 30 cm / 2
= 15 cm
To find the depth of the water in the bowl, we can subtract the horizontal diameter from the vertical diameter.
Given:
Horizontal diameter below water level = 10 cm
Depth of water = Vertical diameter - Horizontal diameter
= 30 cm - 10 cm
= 20 cm
Therefore, the radius of the bowl is 15 cm and the depth of the water in the bowl is 20 cm.
To calculate the radius of the bowl, we need to find the difference between the horizontal diameter and the diameter of the water level, and then divide it by 2.
Let's calculate the radius:
Horizontal diameter = 30 cm
Diameter of water level = Horizontal diameter - 10 cm
= 30 cm - 10 cm
= 20 cm
Radius = (Diameter of water level)/2
= 20 cm/2
= 10 cm
Therefore, the radius of the bowl is 10 cm.
To calculate the depth of the water in the bowl, we need to subtract the radius from the water level's diameter.
Let's calculate the depth:
Depth of water = Diameter of water level - 2 * Radius
= 20 cm - 2 * 10 cm
= 20 cm - 20 cm
= 0 cm
Therefore, the depth of the water in the bowl is 0 cm.