Question

a food vendor sells juice in a cone-shaped paper cup.

which of the following is closest to the maximum volume of juice that this cup can hold?

• 4 \text{ in.}^3
• 16 \text{ in.}^3
• 12 \text{ in.}^3
• 24 \text{ in.}^3

Explanation:

⚡ Using what you learned: volume of prisms, pyramids, cylinders, cones, spheres

Step 1: Identify given dimensions

$$ \text{Diameter } (d) = 3\text{ in.} \implies \text{Radius } (r) = \frac{3}{2} = 1.5\text{ in.} $$

$$ \text{Height } (h) = 5\text{ in.} $$

Step 2: Calculate volume

$$ V = \frac{1}{3}\pi r^2 h $$

$$ V = \frac{1}{3}\pi (1.5)^2 (5) $$

$$ V = \frac{1}{3}\pi (2.25)(5) = 3.75\pi \approx 11.78\text{ in.}^3 $$

Step 3: Compare with options

The value \(11.78\text{ in.}^3\) is closest to \(12\text{ in.}^3\).

Answer:

\(12\text{ in.}^3\)