Question

find the surface area of this cone. use 3.14 for π. cone diagram with 6 m, 4 m, formulas: la=πrl, sa=la+b sa = ? m² round your answer to the nearest tenth.

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 \( LA = \pi r l \), where:

• \( r = 4 \, \text{m} \) (radius of the base),
• \( l = 6 \, \text{m} \) (slant height),
• \( \pi \approx 3.14 \).

Substitute the values:
\[
LA = 3.14 \times 4 \times 6 = 3.14 \times 24 = 75.36 \, \text{m}^2
\]

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

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

Substitute \( r = 4 \, \text{m} \) and \( \pi \approx 3.14 \):
\[
B = 3.14 \times 4^2 = 3.14 \times 16 = 50.24 \, \text{m}^2
\]

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

Add the lateral surface area and the base area:
\[
SA = LA + B = 75.36 + 50.24 = 125.6 \, \text{m}^2
\]

\( \boldsymbol{125.6} \)