Question

the sugar cone has a height of 5.5 inches and a diameter of 2.5 inches across its circular top. it is filled with ice - cream level to the top. calculate, to the nearest cubic inch, the volume of ice - cream in the cone. a 3 in³ b 9 in³ c 14 in³ d 27 in³ e 36 in³

Explanation:

Step1: Find the radius

The diameter $d = 2.5$ inches, so the radius $r=\frac{d}{2}=\frac{2.5}{2}=1.25$ inches.

Step2: Use the cone - volume formula

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 1.25$ inches and $h = 5.5$ inches into the formula.
$V=\frac{1}{3}\times\pi\times(1.25)^{2}\times5.5$
$V=\frac{1}{3}\times\pi\times1.5625\times5.5$
$V=\frac{1}{3}\times\pi\times8.59375$
$V\approx\frac{8.59375\pi}{3}\approx9$ in³ (rounded to the nearest cubic inch)

Answer:

B. 9 in³