Question

what is the surface area of this cone? round your answer to the nearest hundredth. 54 yd 19 yd square yards submit

Explanation:

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

The surface area \( S \) of a cone is given by the formula \( S=\pi r(r + l) \), where \( r \) is the radius of the base and \( l \) is the slant height of the cone.

Step2: Identify the values of \( r \) and \( l \)

From the diagram, the radius \( r = 19\) yd and the slant height \( l=54\) yd.

Step3: Substitute the values into the formula

First, calculate \( r + l=19 + 54=73\) yd.
Then, calculate \( \pi r(r + l)=\pi\times19\times73\).
We know that \( \pi\approx3.14159\), so \( 3.14159\times19\times73\).
First, calculate \( 19\times73 = 1387\).
Then, calculate \( 3.14159\times1387\approx3.14159\times1387\).
\( 3.14159\times1387 = 3.14159\times(1300 + 87)=3.14159\times1300+3.14159\times87\)
\( 3.14159\times1300 = 4084.067\)
\( 3.14159\times87=273.31833\)
Adding these two results: \( 4084.067+273.31833 = 4357.38533\)

Answer:

\( 4357.39\) (rounded to the nearest hundredth)