Question

The total surface area of a cone is 625 in.2. If the radius of the cone is 5 in., what is the slant height of the cone? Round the answer to the nearest whole number.(1 point)

Answer 1

wrong

Answer 2

The total surface area of a cone is given by the formula:

Surface Area = πr(r + l)

where r is the radius and l is the slant height.

In this problem, the surface area is given as 625 in.² and the radius is 5 in. Plugging these values into the formula, we can solve for the slant height:

625 = π(5)(5 + l)

Dividing both sides by π(5) gives:

125 = 5(5 + l)

Dividing both sides by 5 gives:

25 = 5 + l

Subtracting 5 from both sides gives:

20 = l

Therefore, the slant height of the cone is 20 inches.

Answer 3

I apologize for the mistake. Let's correct it:

The surface area of a cone is given by the formula:

Surface Area = πr(r + l)

where r is the radius and l is the slant height.

In this problem, the surface area is given as 625 square inches and the radius is 5 inches. Plugging these values into the formula, we can solve for the slant height:

625 = π(5)(5 + l)

Dividing both sides by π(5) gives:

625/(5π) = 5 + l

Dividing both sides by 5 gives:

125/π = 1 + l

Subtracting 1 from both sides gives:

125/π - 1 = l

Using a calculator to evaluate the left side, we find:

125/π - 1 ≈ 39.79

Therefore, the slant height of the cone is approximately 39.79 inches, rounded to the nearest whole number. So, the slant height is 40 inches.