Answer: 31.41 square units
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