if the height of a cylinder is doubled and its radius is halved, then what is the percentage change of its new curved surface area to its original surface area.
if the height of a cylinder is doubled and its radius is halved, then what is the percentage change of its new curved surface area to its original surface area.
Answer: Let’s denote the original height of the cylinder as h and the original radius as r. The original curved surface area (A_{\text{original}}) is given by:
A_{\text{original}} = 2\pi r h
When the height is doubled (2h) and the radius is halved (r/2), the new curved surface area (A_{\text{new}}) is given by:
A_{\text{new}} = 2\pi \left(\frac{r}{2}\right) (2h) = 2\pi r h
Notice that the new and original curved surface areas are the same after the changes in height and radius. This is because doubling the height and halving the radius cancels out each other’s effects on the curved surface area.
The percentage change in curved surface area would be:
\text{Percentage Change} = \frac{A_{\text{new}} - A_{\text{original}}}{A_{\text{original}}} \times 100
Substituting the values:
\text{Percentage Change} = \frac{(2\pi r h - 2\pi r h)}{2\pi r h} \times 100 = 0\%
So, the percentage change in the curved surface area is 0%.