Question

tiana would like to buy ice cream cones for her birthday party, but she wants cones with the largest volume. which of the following brands of ice cream cones should she buy?
brand a:
height of cone = 16 cm
radius of cone base = 5 cm
brand b:
height of cone = 20 cm
radius of cone base = 4 cm

a. brand a
b. brand b
c. either — the cones have equal volumes

Explanation:

Step1: Recall cone volume formula

The volume of a cone is $V = \frac{1}{3}\pi r^2 h$, where $r$ is radius, $h$ is height.

Step2: Calculate Brand A volume

Substitute $r=5$, $h=16$:
$V_A = \frac{1}{3}\pi (5)^2 (16) = \frac{1}{3}\pi \times 25 \times 16 = \frac{400}{3}\pi \approx 133.33\pi$

Step3: Calculate Brand B volume

Substitute $r=4$, $h=20$:
$V_B = \frac{1}{3}\pi (4)^2 (20) = \frac{1}{3}\pi \times 16 \times 20 = \frac{320}{3}\pi \approx 106.67\pi$

Step4: Compare the two volumes

$\frac{400}{3}\pi > \frac{320}{3}\pi$, so $V_A > V_B$.

Answer:

A. Brand A