Question

question 20 of 25
tiana would like to buy cone - shaped hats for her birthday party. she wantshats with the largest volume, since they look bigger. which of the followingbrands of hat should she buy?
brand a:
height of cone = 15 in.
radius of cone base = 6 in.
brand b:
height of cone = 18 in.
radius of cone base = 5 in.
a. brand a
b. brand b
c. either - the hats have equal volumes

Explanation:

Step1: Calculate volume of Brand A

Volume formula for cone \(V=\frac{1}{3}\pi r^{2}h\). For Brand A, \(r = 6\) in, \(h=15\) in.
\(V_A=\frac{1}{3}\pi\times6^{2}\times15=\frac{1}{3}\pi\times36\times15 = 180\pi\)

Step2: Calculate volume of Brand B

For Brand B, \(r = 5\) in, \(h = 18\) in.
\(V_B=\frac{1}{3}\pi\times5^{2}\times18=\frac{1}{3}\pi\times25\times18=150\pi\)

Since \(180\pi>150\pi\) (i.e., \(V_A > V_B\)), Brand A has larger volume.

Answer:

A. Brand A