The molten steel will be 31.5 inches high.
Step-by-step explanation:
Step 1; As the molten steel is transferred from the scoop to the cylindrical storage, both the volumes must be equal. The hemisphere's volume is [tex]\frac{2}{3}[/tex] multiplied with π and with the cube of the radius (r³). If the radius is 21 inches.
The volume of the hemisphere = [tex]\frac{2}{3}[/tex] × π × 21 × 21 × 21 = 19,396.193 cubic inches.
Step 2; The cylinder's volume is calculated by multiplying π with the square of the radius (r²) and height (h). If the diameter is 28 inches, the radius equals 14 inches.
The volume of the cylinder = π × 14 × 14 × h = 615.752 × h cubic inches.
Step 3; Now, we substitute the values of both volumes with each other.
The volume of the hemisphere = The volume of the cylinder.
19,396.193 = 615.752 × h,
h = [tex]\frac{19,396.193}{615.752}[/tex] = 31.500 inches.
So the height of the cylinder is 31.50 inches. Rounding this off we get 31.5 inches.
