Question

find the surface area of the cone below.
leave your answer in terms of \\(\pi\\).

surface area of a cone
\\(sa = \pi r \ell + \pi r^2\\)

\\(sa = ? \pi \text{ cm}^2\\)

Explanation:

Identify given values

We are given:

• Height of the cone \(h = 15\text{ cm}\)
• Radius of the base \(r = 8\text{ cm}\)

Find slant height

The height, radius, and slant height \(l\) form a right triangle.
Using the Pythagorean theorem:

$$ l^2 = r^2 + h^2 $$

$$ l^2 = 8^2 + 15^2 = 64 + 225 = 289 $$

$$ l = \sqrt{289} = 17\text{ cm} $$

Calculate surface area

The formula for the total surface area of a cone is:

$$ \text{SA} = \pi r l + \pi r^2 $$

Substitute the values:

$$ \text{SA} = \pi (8)(17) + \pi (8)^2 $$

$$ \text{SA} = 136\pi + 64\pi = 200\pi\text{ cm}^2 $$

Determine missing value

The question asks for the coefficient of \(\pi\) in the surface area expression:

$$ \text{SA} = [?]\pi\text{ cm}^2 $$

Comparing \(200\pi\) with \([?]\pi\), the missing value is \(200\).

Answer:

Find the surface area of the cone below. Leave your answer in terms of \(\pi\).

\(\text{SA} =\) <blank>200</blank> \(\pi\text{ cm}^2\)