A Hemisphere Bolw Of Diameter 30cm Has The Same Volume As A Cylinder Of Height 22.5cm. Find The Radius Of The Cylinder

(2/3)*3.14*(30/2)^3=3.14*r^2*22.5

7069 = 70.69r^2.
r^2 = 100.
r = 10 cm.

To find the radius of the cylinder, we first need to calculate the volume of both the hemisphere and the cylinder, using their respective formulas.

The formula for the volume of a hemisphere is: V = (2/3) * π * r^3
The formula for the volume of a cylinder is: V = π * r^2 * h

Given information:
Diameter of the hemisphere = 30 cm
Height of the cylinder = 22.5 cm

Let's start by finding the volume of the hemisphere.

Step 1: Find the radius of the hemisphere
The diameter is given as 30 cm, so the radius (r) is half of the diameter.
r = 30 cm / 2
r = 15 cm

Step 2: Calculate the volume of the hemisphere
V_h = (2/3) * π * r^3
V_h = (2/3) * π * (15 cm)^3
V_h ≈ 2 * 3.14 * (3375 cm^3)
V_h ≈ 21150 cm^3

Now, let's find the volume of the cylinder.

Step 1: Calculate the volume of the cylinder, using the formula V = π * r^2 * h.
21150 cm^3 = π * r^2 * 22.5 cm

Step 2: Rearrange the formula to solve for r.
r^2 = (21150 cm^3) / (π * 22.5 cm)
r^2 ≈ 300 cm^2

Step 3: Find the square root of both sides to get the value of r.
r ≈ √(300 cm^2)
r ≈ 17.32 cm

Therefore, the radius of the cylinder is approximately 17.32 cm.