Question

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled then what will happen to total surface area.

Answer 1

Answer:

The total surface area of a cylinder is equal to 2πr(r+h).

Step-by-step explanation:

Now, if the conditions are normal, then the area remains 2πr(r+h),

But when the demensions are edited, then,

Newer height = 1/4 of previous height.

and new radius = 2* Previous radius.

then, I substitute the values of height and radius,

Then newer area = 2π * 2r(2r+h/4),

Now, I compare the areas by diving each other,

$\frac{older \: area}{newer \: area} = \frac{2\pi \: r(r + h)}{4\pi \: r(2r + \frac{h}{2} )} = \frac{r + h}{4r + \frac{h}{2} }$

Now, I assume the radius to be 1 cm,

and height be 2 cm.

then, our fraction becomes,

$\frac{1 + 2}{4(1) + \frac{2}{2} } = \frac{3}{4 + 1} = \frac{3}{5}$

so, the area becomes 5/3 of the original value.