Question

choose the formula that franken can use to determine the volume of the flask.

• (v = pi(1.2)^2(3.8) + \frac{4}{3}pi(3.4)^3)
• (v = pi(0.6)^2(3.8) + \frac{4}{3}pi(1.7)^3)
• (v = pi(0.6)^2(1.9) + \frac{4}{3}pi(1.7)^3)
• (v = \frac{4}{3}pi(1.2)^2(7.2))

Explanation:

⚡ Using what you learned: Composite Figures: Area, Surface Area, Volume

Step 1: Identify the component shapes

The flask is a composite 3D shape made of two standard geometric solids:

1. A cylinder at the top (the neck of the flask).
2. A sphere at the bottom (the body of the flask).

The total volume \( V \) is the sum of the volume of the cylinder and the volume of the sphere:

$$ V = V_{\text{cylinder}} + V_{\text{sphere}} $$

Step 2: Identify the dimensions of each shape

From the diagram:

• Cylinder (neck):
• Radius \( r = 0.6\text{ m} \)
• Height \( h = 3.8\text{ m} \)

• Sphere (body):
• Radius \( r = 1.7\text{ m} \)

Step 3: Apply the volume formulas

• Volume of a cylinder:

$$ V_{\text{cylinder}} = \pi r^2 h = \pi (0.6)^2 (3.8) $$

• Volume of a sphere:

$$ V_{\text{sphere}} = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (1.7)^3 $$

Combining these gives:

$$ V = \pi (0.6)^2 (3.8) + \frac{4}{3} \pi (1.7)^3 $$

Answer:

$$ V = \pi(0.6)^2(3.8) + \frac{4}{3}\pi(1.7)^3 $$