Question

A can of beans has surface area 337 cm2. It's heights is 11cm. What is the radius of the circular top?

Answer 1

3.66 cm

Explanation:

r = Radius of cylinder

h = Height of the cylinder = 11 cm

A = Total surface area of the cylinder =
`337\ \text{cm}^2`

Total surface area of a cylinder is given by

`A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r(r+h)\\\Rightarrow (A)/(2\pi)=r^2+rh\\\Rightarrow r^2+rh-(A)/(2\pi)=0\\\Rightarrow r^2+11r-(337)/(2\pi)=0\\\Rightarrow r^2+11r-53.64=0\\\Rightarrow 100r^2+1100r-5364=0\\\Rightarrow r=(-1100\pm √(1100^2-4* 100\left(-5364\right)))/(2* 100)\\\Rightarrow r=3.66,-14.65`

So, the radius of the circular top is 3.66 cm.