Question

find the lateral area of the cone shown, to the nearest whole number.

Explanation:

Step1: Identify formula for lateral area of cone

The formula for the lateral (or curved) surface area of a cone is \( LA=\pi rl \), where \( r \) is the radius of the base and \( l \) is the slant height.
From the diagram, the diameter of the base is \( 9\space mm \), so the radius \( r = \frac{9}{2}= 4.5\space mm \), and the slant height \( l = 20\space mm \).

Step2: Substitute values into the formula

Substitute \( r = 4.5 \) and \( l = 20 \) into the formula \( LA=\pi rl \):
\( LA=\pi\times4.5\times20 \)

Step3: Calculate the value

First, calculate \( 4.5\times20 = 90 \). Then, multiply by \( \pi \): \( LA = 90\pi \approx 90\times3.1416 \approx 282.744 \). Rounding to the nearest whole number gives \( 283 \space mm^2 \).

Answer:

\( 283\space mm^2 \)