Question

In a cylinder, radius is doubled and height is halved, curved surface area will
A. halved
B. doubled
C. same
D. four times

Answer 1

Hint:A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape and the center of the two bases are joined by a line segment, which is called the axis. The formula of the surface area of a cylinder is $2\pi rh$ , where $r$ is the radius of the cylinder and $h$ is the height of the cylinder . First we find the given conditions and then we find the difference in the curved surface area before and after using the given condition.

Complete step by step answer:
Let $r$ be the radius of the cylinder and $h$ be the height of the cylinder.Then the curved surface area of the cylinder is $2\pi rh$ square units.Now we use the given condition i.e., the radius is doubled i.e., $R = 2r$. And the height of the cylinder is halved i.e., $H = \dfrac{h}{2}$.

Now we find the curved surface area of the cylinder after using the condition
$2\pi \times R \times H$
$\Rightarrow 2\pi \times 2r \times \dfrac{h}{2}$
Now $2$ and $\dfrac{1}{2}$ will be canceled and we get
$2\pi \times r \times h$
$\therefore 2\pi rh$ square units
Therefore the curved surface area before using the condition and the surface area after using the condition will be the same.

Therefore the option C is correct.

Note:When we solve this type of question , we take care about what is asked . There are two types of surface area in a cylinder: one is the curved surface area of a cylinder and the other is total surface area of a cylinder. First we observe and then we solve . The formula of the total surface area of a cylinder is the sum of the curved surface area of a cylinder and the area of the base circle.