Question

find the surface area of this cone. use 3.14 for π. 5 cm 3 cm surface area of a cone la = πrl sa = la + b sa = ? cm² round your answer to the nearest

Explanation:

Answer:

To find the surface area of the cone, we use the formula \( SA = LA + B \), where \( LA \) is the lateral (or curved) surface area and \( B \) is the area of the base.

Step 1: Calculate the lateral surface area (\( LA \))

The formula for the lateral surface area of a cone is \( LA = \pi r \ell \), where \( r \) is the radius and \( \ell \) is the slant height.
Given:

• Radius \( r = 3 \) cm
• Slant height \( \ell = 5 \) cm
• \( \pi \approx 3.14 \)

Substitute the values into the formula:
\( LA = 3.14 \times 3 \times 5 \)
\( LA = 3.14 \times 15 \)
\( LA = 47.1 \) cm²

Step 2: Calculate the area of the base (\( B \))

The base of a cone is a circle, so the area of the base is \( B = \pi r^2 \).

Substitute \( r = 3 \) cm and \( \pi \approx 3.14 \):
\( B = 3.14 \times (3)^2 \)
\( B = 3.14 \times 9 \)
\( B = 28.26 \) cm²

Step 3: Calculate the total surface area (\( SA \))

Add the lateral surface area and the base area:
\( SA = LA + B \)
\( SA = 47.1 + 28.26 \)
\( SA = 75.36 \) cm²

\( \boldsymbol{75.36} \)