Question

You remove the lid of the can. What is the percent of change in the surface area of the can?

Answer 1

Hint:

Step 1: Given that: Diameter $=85mm$

So Radius $=\frac{85}{2}mm$

Radius $=42.5mm$

And height of can $=40mm$

Step 2: The surface area of the can $=2{\mathrm{\pi r}}^2+2\mathrm{\pi rh}$

The surface area of the can $=(2\times 3.14\times 42.5\times 42.5+2\times 3.14\times 42.5\times 40)m{m}^2$

The surface area of the can $=(11343.25+10676)m{m}^2$

$=22019.25m{m}^2$

Step 3: Now the area of the lid $={\mathrm{\pi r}}^2$

$$\begin{gathered} =3.14\times 42.5\times 42.5m{m}^2 \\ =5671.625m{m}^2 \end{gathered}$$

.Step 4: If we remove the lid, then the % change will be $=\frac{5671.625}{22019.25}\times 100=25.75\%$

Final answer: The percentage change in the surface area after removing the lid is 25.75 %