Question

find the surface area of the right cone. round your answer to the nearest hundredth. 7.2 cm 11 cm the surface area is about square centimeters.

Explanation:

Step1: Find the radius of the cone

The diameter of the base is 11 cm, so the radius \( r=\frac{11}{2} = 5.5\) cm.

Step2: Recall the formula for the surface area of a cone

The surface area \( S\) of a right cone is given by \( S=\pi r^{2}+\pi rl\), where \( r\) is the radius and \( l\) is the slant height. Here, \( l = 7.2\) cm, \( r = 5.5\) cm.

Step3: Calculate the base area (\(\pi r^{2}\))

\(\pi r^{2}=\pi\times(5.5)^{2}=\pi\times30.25\approx3.1416\times30.25\approx95.033\)

Step4: Calculate the lateral (side) surface area (\(\pi rl\))

\(\pi rl=\pi\times5.5\times7.2=\pi\times39.6\approx3.1416\times39.6\approx124.344\)

Step5: Sum the two areas to get the total surface area

\( S=95.033 + 124.344=219.377\approx219.38\) (rounded to the nearest hundredth)

Answer:

\(219.38\)