Answer:
Here’s the response provided
Step-by-step explanation:
Referring to the flask diagram, the diameter of the cylinder measures 1 inch and its height (h) is 3 inches. Thus, the radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch
The volume of the cylinder can be calculated as πr²h = π(0.5)² × 3 = 2.36 in³
As for the sphere, its diameter is 4.5 in. Hence, the radius of the sphere R = diameter / 2 = 4.5/2 = 2.25 in
The volume of the sphere is calculated as 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³
The total volume of the flask = Volume of the cylinder + Volume of the sphere = 2.36 + 47.71 = 50.07 in³
<pWhen the cylinder and the sphere are expanded by a scale factor of 2, the height (h') of the cylinder becomes 3/2 = 1.5 inches and the radius (r') becomes 0.5/2 = 0.025 inches.
The new volume for the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³
For the sphere, the new radius is R' = 2.25 / 2 = 1.125 in.
The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³
Thus, the new volume of the flask = The new volume of the cylinder + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³
<pThe ratio of the new volume to the original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125<pThe resulting volume will thus be 0.125 times the original volume
