Question

The radius of a cone is 3cm and vertical height is 4cm. Find the area of curved surface area.

Answer 1

Hint: Here, we will draw a figure of a cone given with the parameters like radius r is 3cm and height h is 4cm. Then, we will find the slant height of the cone using the formula $\sqrt{{{r}^{2}}+{{h}^{2}}}=l$ . After this, we will use the formula of curved surface area as $CSA=\pi rl$ and get the required answer.

Complete step-by-step answer:

We are given that radius $r=3cm$ and height $h=4cm$ . So, figure will be as below:

Now, we have to find value of slant height which we will get by using the formula $\sqrt{{{r}^{2}}+{{h}^{2}}}=l$
So, on substituting the values in the formula we get
$\sqrt{{{3}^{2}}+{{4}^{2}}}=l$
On further simplifying, we get
$\sqrt{9+16}=l$
$\sqrt{25}=\sqrt{{{5}^{2}}}=l$
Therefore, the value of slant height is $l=5cm$ .
Now, we have to find the area of the curved surface of the cone. So, we will use the formula of curved surface area as $CSA=\pi rl$ . On substituting the values, we get
$CSA=\pi \times 3\times 5$
$CSA=\pi \times 15$
Now, we are not told any specific value of $\pi $ so, we will use 3.14 and on solving we get
$CSA=3.14\times 15=47.1c{{m}^{2}}$
Thus, the curved surface area of the cone is $47.1c{{m}^{2}}$ .

Note: Remember that the value of $\pi $ is not specified here. So, if the answer we write as $15\pi $ then also it is correct. But for proper value we will take $\pi $ as 3.14. Sometimes, there are chances that in curved surface area students include the area of base also i.e. $\pi rl+\pi {{r}^{2}}$ and then calculate the area. This is the wrong formula and will lead to the wrong answer. So, remember all the formulas carefully so that this type of mistake does not happen.