A measuring cylinder is full of water that is to be poured into a pan with a rectangular base. The dimensions of the base of the pan are 15 inches × 10 inches and the height of the pan is 3 inches. The height of the measuring cylinder is 15 inches. If the water from the measuring cylinder exactly fills the pan, then find the radius of the circular base of the measuring cylinder.

The dimension of the given pan = 15 inches × 10 inches x 3 inches

Volume of the pan = length x breadth x height

Volume of the pan = (15 × 10 × 3) inch³

                                  = 450 inch³

Volume of a cylinder = π × r²  x height

Volume of the measuring cylinder = (π × r² × 15) inch³

The volume of the pan equals the volume of the measuring cylinder.

∴ 450 inch³ = (π × r² × 15) inch³

$$\begin{gathered} r^2=\frac{450}{3.14\times 15}=9.55 \\ r=\sqrt{9.55}\approx 3.1 \mathrm{in} \end{gathered}$$

Thus, the radius of the circular base of the measuring cylinder = 3.1 inches.