Question

The curved surface area of a right circular cylinder of height 14 cm is 88 cm\[^2\]. Find the diameter of the base of the cylinder.

Answer 1

Hint: First, we will find the radius of the roller from the given diameter. Then we will use the formula of the curved surface area of circle \[2 \pi rh\] and then multiply it by \[n\] to find the area covered in \[n\] revolutions.

Complete step by step solution: We are given that the height of the cylinder \[h\] is 14 cm and the curved surface area is 88 cm\[^2\].

Let us assume that the diameter of the base of the cylinder is \[d\] cm.

We know that the curved surface area of the right circular cylinder is \[2\pi rh\], where \[r\] is the radius of the base of the cylinder and \[h\] is the height of the cylinder.

Also, the curved surface area of the cylinder is 88, so we have

\[2\pi rh = 88\]

From this we can now find the radius of the cylinder by substituting the values of \[h\] in the above equation, we get

\[
   \Rightarrow 2\pi r \times 14 = 88 \\
   \Rightarrow 28\pi r = 88 \\
 \]

Dividing the above equation by \[28\pi \]on both sides, we get
\[
   \Rightarrow \dfrac{{28\pi r}}{{28\pi }} = \dfrac{{88}}{{28\pi }} \\
   \Rightarrow r = \dfrac{{22}}{{7\pi }} \\
 \]

Substituting the value of \[\pi \] in the above equation, we get

\[
   \Rightarrow r = \dfrac{{22}}{{7 \times \dfrac{{22}}{7}}} \\
   \Rightarrow r = 1 \\
 \]

Thus, the radius of the right circular cylinder is 1 cm.

Now we know that the diameter of the base is \[2r\].

So we will now find the diameter of the cylinder \[d\] by multiplying the value of radius by 2, we get

\[
   \Rightarrow d = 2 \times 1 \\
   \Rightarrow d = 2{\text{ cm}} \\
 \]

Hence, the diameter of the given right circular cylinder is 2 cm.

Note: We should make a diagram to understand the given question properly. In this question, some students don’t read the question carefully and end up finding the radius of the given cylinder, which is wrong. We have to multiply the radius by 2 to find the diameter of the cylinder or else the final answer will be wrong. Students should always remember to write the units.