Question

select the correct answer.
a vase is in the shape of a cone. the height is 12 inches and the diameter is 4.4 inches.
what is the lateral surface area to the nearest tenth of a square inch?
84.3 square inches
168.6 square inches
99.5 square inches
149.1 square inches

Explanation:

Step1: Find the radius

The diameter \(d = 4.4\) inches. The radius \(r=\frac{d}{2}=\frac{4.4}{2}=2.2\) inches.

Step2: Find the slant height \(l\)

Using the Pythagorean theorem \(l=\sqrt{r^{2}+h^{2}}\), where \(h = 12\) inches and \(r = 2.2\) inches.
\(l=\sqrt{(2.2)^{2}+12^{2}}=\sqrt{4.84 + 144}=\sqrt{148.84}\approx12.2\) inches.

Step3: Calculate the lateral surface area \(A_{l}\)

The formula for the lateral surface area of a cone is \(A_{l}=\pi rl\).
Substitute \(r = 2.2\) inches and \(l\approx12.2\) inches.
\(A_{l}=\pi\times2.2\times12.2\approx3.14\times2.2\times12.2 = 3.14\times26.84=84.3\) square inches.

Answer:

84.3 square inches