A cylinder has a volume of 288 pi cubic meters and a height of 9 meters. What is the area of the base? 32 pi square meters 18 pi square meters 279 pi square meters 2,592 pi square meters

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.

Learn more about volume of cylinder here :

https://brainly.com/question/16134180

#SPJ5