A right cone has an altitude of 4 units and a base diameter of 6 units. What is its lateral area?

31.41 square units

Step-by-step explanation:

Hi, to answer this question we have t apply the next formula:

Lateral area of a right cone = π x slant height x radius

Radius = diameter /2 = 4 /2 = 2 units

To find the slant height:

Since the altitude, slant and radius forms a right triangle we have to apply the Pythagorean Theorem:  

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (in this case the slant) and a and b are the other sides.  

Replacing with the values given:  

c^2 = 4^2 + 3^2  

c^2 = 16 +9

c^2 = 25

c = √25

c = 5 units (slant)

Back with the Lateral area formula:

Lateral area of a right cone (LA) = π x slant height x radius

LA = π x 5 x 2 = 31.41 square units