A bucket in the shape of a frustum has a bottom radius of 15 cm and a top radius of 20 cm. Its vertical depth is 30 cm. If the water from this bucket is poured into a cylindrical container with a base

The bottom radius ($r_1$) is 15 cm.
The top radius ($r_2$) is 20 cm.
The vertical depth ($h_f$) is 30 cm.
We will use $\pi = \frac{22}{7}$.

The formula for the volume of a frustum is $V_f = \frac{1}{3}\pi h_f (r_1^2 + r_1 r_2 + r_2^2)$.
Substitute the given values:

The base radius ($R$) of the cylinder is 20 cm.
Let the depth of the water in the cylinder be $H$.

The volume of water in the cylinder is $V_c = \pi R^2 H$.
Since the water is poured from the frustum into the cylinder, $V_c = V_f$.

Substitute $R = 20$ and $\pi = \frac{22}{7}$:

Multiply both sides by 7 to cancel the denominators:

Divide by 8800:

Simplify the fraction by dividing both numerator and denominator by 11:

Convert the fraction to a decimal:

The depth of the water in the cylindrical container is 23.125 cm.