Question

A can of beans has surface area 332 cm squared. Its height is 11 cm. What is the radius of the circular​ top? (Hint: The surface area consists of the circular top and bottom and a rectangle that represents the side cut open vertically and​ unrolled.)

Answer 1

surface area=circumference*height+2*area of a circular base

SA=C*h+2*pi*r^2

SA=(2*pi*r)*h+2*pi*r^2

396=(2*pi*r)*20+2*pi*r^2

396=40*pi*r+2*pi*r^2

divide both sides by 2

198=20*pi*r+pi*r^2

factor out pi*r on the right side

198=(pi*r)*(20+r)

use 22/7 for pi instead of 3.14, it doesn't matter which approx. for pi you use

I'm using 22/7 because 198 is divisible by 22

198=(22/7)(r)(20+r)

multiply both sides by 7/22

(7/22)(198)=(7/22)(22/7)(r)(20+r)

7*9=(r)(20+r)

63=20r+r^2

r^2+20r-63=0

use the quadratic formula

(-20±√400+252)/2

(-20+√652)/2

(-20+25.53429)/2

5.53429/2

2.767 cm is the radius r

you can use 3.14 if you like, or any other approx. for pi, and get approximately the same answer

I checked my work using r=2.767 and got 395.53 for the surface area which is almost 396 !

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