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

Answer:

3.66 cm

Step-by-step 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

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r(r+h)\\\Rightarrow \dfrac{A}{2\pi}=r^2+rh\\\Rightarrow r^2+rh-\dfrac{A}{2\pi}=0\\\Rightarrow r^2+11r-\dfrac{337}{2\pi}=0\\\Rightarrow r^2+11r-53.64=0\\\Rightarrow 100r^2+1100r-5364=0\\\Rightarrow r=\dfrac{-1100\pm \sqrt{1100^2-4\times 100\left(-5364\right)}}{2\times 100}\\\Rightarrow r=3.66,-14.65$

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