Answer:
Explanation:
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height. Since both cylinders have the same base area, we can assume they have the same radius, which we'll call r.
For Cylinder A, we know the volume is 6 cubic units and the height is 3 units. So we can use the formula for volume to find the radius:
V = πr^2h
6 = πr^2(3)
2 = πr^2
r^2 = 2/π
r ≈ 0.7979
Now we can use this radius to find the volume of Cylinder B. We know that the height is the same as Cylinder A, and we know the slant height is 4 units. The slant height is related to the radius and height by the Pythagorean theorem: s^2 = r^2 + h^2. Since we know the height and radius for both cylinders, we can solve for the slant height of Cylinder B:
s^2 = r^2 + h^2
16 = r^2 + 3^2
16 = r^2 + 9
r^2 = 7
r ≈ 2.6458
Now we can use the formula for volume to find the volume of Cylinder B:
V = πr^2h
V = π(2.6458)^2(3)
V ≈ 62.8318
Therefore, the volume of Cylinder B is approximately 62.8318 cubic units.