Question

what is the volume of a cone with radius 4.2 in. and height 1.4 ft? a) 26 in.³ b) 310 in.³ c) 1241 in.³ d) 931 in.³

Explanation:

Step1: Convert height to inches

Since 1 foot = 12 inches, 1.4 ft = 1.4×12 = 16.8 inches.

Step2: Recall volume formula for cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius and $h$ is the height. Here $r = 4.2$ inches and $h=16.8$ inches.

Step3: Substitute values into formula

$V=\frac{1}{3}\times\pi\times(4.2)^{2}\times16.8$. First, $(4.2)^{2}=17.64$. Then $V=\frac{1}{3}\times\pi\times17.64\times16.8$.
$V=\frac{1}{3}\times\pi\times296.352$.
$V = 98.784\pi$. Taking $\pi\approx3.14$, we have $V\approx98.784\times3.14 = 310.18176\approx310$ in³.

Answer:

B. 310 in³