Water is poured into a hemispherical bowl with a radius of 30cm. The water's depth is 12cm. Calculate the radius of the surface of the water
draw a semi-circle
mark in the centre O and label the horizontal radius 30
If the water level is 12 cm deep then the distance from the centre to the water level is 18 cm
draw in a radius to the end of the water level and you have a right-angled triangle, with sides 18 and r, where r is the radius of the water-level, and the hypotenuse is 30
go for it !
To calculate the radius of the surface of the water, we need to find the radius of the hemisphere that is submerged in the water.
Given:
Radius of the hemispherical bowl (R) = 30 cm
Depth of the water (h) = 12 cm
We can use the Pythagorean theorem to find the radius of the surface of the water.
Let r be the radius of the surface of the water.
Using Pythagorean theorem, we have:
R^2 = r^2 + (R - h)^2
Substituting the given values, we get:
30^2 = r^2 + (30 - 12)^2
900 = r^2 + 18^2
900 = r^2 + 324
r^2 = 900 - 324
r^2 = 576
Taking the square root of both sides, we get:
r = √576
r = 24 cm
Therefore, the radius of the surface of the water is 24 cm.
To calculate the radius of the surface of the water, we need to consider the shape of the bowl and the depth of the water.
The bowl is a hemisphere, which means it is half of a sphere. The radius of the hemisphere is given as 30 cm.
The water's depth is given as 12 cm. This means that the water level rises 12 cm from the bottom of the hemisphere.
To find the radius of the water's surface, we need to subtract the depth of the water from the radius of the hemisphere.
So, the radius of the water's surface can be calculated as:
Radius of water's surface = Radius of hemisphere - Depth of water
= 30 cm - 12 cm
= 18 cm
Therefore, the radius of the surface of the water is 18 cm.