Question

The total surface area of a cone 704 sq.cm & radius of its base is 7 cm. Find the slant height of the cone.$\left(\pi ={\displaystyle \frac{22}{7}}\right)$

Answer 1

Hint: In order to solve this question, one should identify the given dimensions of cone and also remember to use the formula for Total surface area of cone i.e. $\pi r\left(l+r\right)$, using this information will help you to approach the solution of the problem.

Complete step by step answer:

In question we should know the very base of this question, that is its formula$\pi r\left(l+r\right)$. If you know the formula, you should be able to solve the question.
But another thing to know is how to form its equation. It is pretty simple but can become confusing at times so the first step of this question is very important as this step makes or breaks your question.
But rather than that you should be sure of the values as they determine the answer. These basic steps will help you to solve the question.
Total surface area of cone =$704\text{ c}{\text{m}}^2$.
$\Rightarrow$$\pi r\left(l+r\right)=704\Rightarrow {\displaystyle \frac{22}{7}}\times 7\left(l+7\right)=704$
$\Rightarrow$$$22l+154=704$$
$\Rightarrow$$$22l=550$$
$\Rightarrow$$$l={\displaystyle \frac{550}{22}}$$
$\Rightarrow$l = 25 cm
Hence, the height of the cone is 25 cm.
Note:
In the above solution we came across the term “cone” which can be described as the three-dimension shape which is formed by the sets of lines which is consist a same point and apex or vertex, it consist of a circular base and the distance from the vertex of the cone to the center of the base is the height of the cone there are different types of cones such as right circular cone, oblique cone. The properties of the cone consists of one face which is the circular base with no edges on it and it consists of either one vertex or one apex.