We want to find Enrique's mistake and correct it. To do so, we will calculate the total surface area of the traffic cone. Let's start by drawing the cone. We know that it has a diameter of $10$ inches and a slant height of $12$ inches.

Recall that the surface area of a cone is the lateral area plus the area of the base. To calculate the surface area of a cone, we can use the following formula.

S . A . = π r ℓ + π r^{2}

In this formula,

r

is the radius 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 .

r = \frac{d}{2}

Substitute

$d = 10$

r = \frac{1 0}{2}

CalcQuot

Calculate quotient

r = 5

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.

Exercise