Question

find the surface area of this cone. use 3.14 for π. 7 cm 3 cm surface area of a cone la = πrl sa = la + b sa = ? cm² 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:

• \( r = 3 \) cm (radius of the base),
• \( l = 7 \) cm (slant height of the cone),
• \( \pi \approx 3.14 \).

Substitute the values into the formula:
\[
LA = 3.14 \times 3 \times 7
\]
\[
LA = 3.14 \times 21
\]
\[
LA = 65.94 \, \text{cm}^2
\]

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

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

Substitute \( r = 3 \) cm and \( \pi \approx 3.14 \):
\[
B = 3.14 \times (3)^2
\]
\[
B = 3.14 \times 9
\]
\[
B = 28.26 \, \text{cm}^2
\]

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

Add the lateral surface area and the base area:
\[
SA = LA + B
\]
\[
SA = 65.94 + 28.26
\]
\[
SA = 94.2 \, \text{cm}^2
\]

So, the surface area of the cone is \(\boldsymbol{94.2}\) square centimeters.