Answer:
The area base of the cylinder is 32 pi square meters which is correct option(A).
Explanation:
The volume of a cylinder is equal to the product of area of circular base and height of a cylinder. The volume of a cylinder is defined as the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it
V = A × h, where
A = area of the base
h = height
The base of a circular cylinder is a circle and the area of a circle of radius 'r' is πr². Thus, the volume (V) of a circular cylinder, using the formula, is, V = πr²h
where , 'r' is the radius of the base (circle) of the cylinder
'h' is the height of the cylinder
π is a constant whose value is either 22/7 (or) 3.142.
Given data,
The volume of cylinder = 288π cubic meters
V = πr²h
Substitute the value of V in the formula
288π = π(r²)(9)
Divided by π both the sides,
288 = 9 r²
288/9 = r²
32 = r²
r² = 32
r ≈ 5.65 meters
The area base (circle) of the cylinder = πr²
Substitute the value of r in the formula,
The area base of the cylinder = π(5.65)²
The area base of the cylinder = π(32)
The area base of the cylinder = 32π
Hence, the area base of the cylinder is 32π square meters.
hope this helps gangy