Question

what is the lateral area of a right cone with a slant height of 12 units and a base radius of 2 units?
○ 75 units squared
○ 50 units squared
○ 88 units squared

Explanation:

Step1: Recall the formula for the lateral area of a right cone

The formula for the lateral (or curved) surface area of a right cone is \( L = \pi r l \), where \( r \) is the radius of the base and \( l \) is the slant height.

Step2: Substitute the given values into the formula

We are given that \( r = 2 \) units and \( l = 12 \) units. Substituting these values into the formula, we get \( L=\pi\times2\times12 = 24\pi\).

Step3: Approximate the value of \( 24\pi \)

Using \( \pi\approx\frac{22}{7} \), we calculate \( 24\times\frac{22}{7}=\frac{528}{7}\approx75.43 \). Among the given options, 75 units squared is the closest approximation.

Answer:

75 units squared