We want to find Enrique's mistake and correct it. To do so, we will calculate the of the traffic . Let's start by drawing the cone. We know that it has a of 10 inches and a of 12 inches.
Recall that the is the plus the area of the base. To calculate the surface area of a cone, we can use the following formula.
S.A.=πrℓ+πr2
In this formula,
r is the of the base and
ℓ is the slant height of the cone. Note that we know the slant height and the diameter of the traffic cone. To find the radius, we can divide the diameter by
2.
Therefore, the radius is
5 inches. Now we can substitute the slant height and the radius into the formula.
S.A.=π(5)(12)+π(5)2
Let's take a closer look at Enrique's solution.
We can see that Enrique used the formula incorrectly. It looks like he substituted the diameter of the cone instead of the radius of the cone in the formula. Let's circle his mistake.
Next, we will calculate the surface area correctly.
S=π(5)(12)+π(5)2
S=π(5)(12)+π(25)
S=60π+25π
S=85π
S=267.035375…
S≈267.04
We got that the surface area of the traffic cone is about
267.04 square inches.