A powdered drink mix is stored in a cylindrical container that has a radius of 6 centimeters and a height of 14 centimeters. Which is closest to the maximum number of cubic centimeters the container will hold?

V=area of base times height

height=height

area of base=area of circle=pir^2

V=hpir^2

r=6

h=14

V=14pi6^2

V=14pi36

V=504pi

aprox pi=3.141592

V=1583.3 round

V=1583 cm^3

Basics of a circle of radius r = 6cm

A - area baze

A = πr² = π (6cm) ² = 36πcm²

2A (upper and lower base) = 2 * 36πcm² = 72πcm²

lateral surface is a rectangle. Side, and the length - lof the circle and side b is the height h of the cylinder.

l = 2πr = 2*π*6cm = 12πcm

h = 14cm

Ar - a rectangle

Ar = l*h = 12πcm * 14cm = 168πcm²

Area cylindrical

2A + Ar = 72πcm² + 168πcm² = 240πcm²

V = A*h = 36πcm² * 14cm = 504πcm³