Question

what is the surface area of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 10 cm 7 cm square centimeters submit

Explanation:

Step1: Recall the formula for the surface area of a cone

The surface area \( S \) of a cone is given by the sum of the lateral (or curved) surface area and the base area. The formula is \( S=\pi r l+\pi r^{2} \), where \( r \) is the radius of the base, \( l \) is the slant height of the cone.

From the diagram, we can see that the radius \( r = 7\space\text{cm}\) and the slant height \( l=10\space\text{cm}\), and \( \pi\approx3.14 \).

Step2: Calculate the lateral surface area

The lateral surface area \( LSA=\pi r l \). Substitute \( r = 7\), \( l = 10\) and \( \pi\approx3.14 \) into the formula:
\( LSA=3.14\times7\times10=3.14\times70 = 219.8\space\text{cm}^2\)

Step3: Calculate the base area

The base of a cone is a circle, and the area of a circle is \( A=\pi r^{2} \). Substitute \( r = 7\) and \( \pi\approx3.14 \) into the formula:
\( A = 3.14\times7^{2}=3.14\times49=153.86\space\text{cm}^2\)

Step4: Calculate the total surface area

The total surface area \( S=LSA + A \). Substitute the values of \( LSA \) and \( A \) we calculated:
\( S=219.8+153.86 = 373.66\space\text{cm}^2\)

Answer:

\( 373.66 \)