Question

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?

Answer 1

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

Answer 2

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