A glass in the form of a frustrum of a cone is represented by a diagram. The glass contains water to a height of 9cm. The bottom of the glass is a circle of radius 2cm while the surface of the water is a circle of radius 6cm. Calculate the volume of the water in the glass

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In about a minute you can get the derivation of the handy formula
v = 1/3 πh (R^2 + Rr + r^2)
where
h = height of frustrum
r = small radius
R = large radius

Or, you can go the long way around and calculate the volume of the whole cone, then subtract the volume of the tip which was cut off.

To calculate the volume of the water in the glass, we can use the formula for the volume of a frustrum of a cone.

The formula for the volume of a frustrum of a cone is given by:

V = (1/3) * π * (R1^2 + R2^2 + (R1 * R2)) * h

Where:
V = Volume of the frustrum of a cone
π = Pi, approximately 3.14159
R1 = Radius of the bottom circle of the frustrum of a cone
R2 = Radius of the top circle of the frustrum of a cone
h = Height of the frustrum of a cone

Given:
R1 = 2 cm (radius of the bottom circle)
R2 = 6 cm (radius of the top circle)
h = 9 cm (height of the frustrum of a cone)

Plugging in the values into the formula, we get:

V = (1/3) * π * (2^2 + 6^2 + (2 * 6)) * 9

Simplifying the equation, we have:

V = (1/3) * π * (4 + 36 + 12) * 9

V = (1/3) * π * 52 * 9

V = (1/3) * π * 468

Now, we can carefully calculate the volume:

V ≈ 1.0472 * 468

V ≈ 489.4008 cm^3

Therefore, the volume of water in the glass is approximately 489.4008 cm^3.