This statement is false.
To understand why, let’s break down the formulas for the lateral surface areas of both shapes.
The lateral surface area of a cone is given by the formula:
Acone = πrl
where r is the radius of the base of the cone and l is the slant height.
On the other hand, the lateral surface area of a cylinder is calculated using the formula:
Acylinder = 2πrh
where r is the radius of the base and h is the height of the cylinder.
Since these formulas involve different dimensions (slant height for the cone and height for the cylinder), their areas will not be equal unless specific conditions are met, which is not generally the case. Therefore, it is not accurate to say that the lateral surface area of cone A is exactly the same as that of cylinder B.