Question

What is the lateral area and surface area of a right cone with radius \[6cm\] and slant height \[13cm\]?

Answer 1

Hint: In the above question, we are given the radius and the slant height of a cone. And we have to calculate the lateral area as well as the surface area of the given cone. We know that the equation of lateral area of a cone is \[\pi rl\]. We will substitute the values of \[r=6cm\] and \[l=13cm\], to get the lateral area of the given cone. Next, we know that the equation of the surface area of the cone is \[\pi r\left( r+l \right)\]. We will substitute the values of \[r=6cm\] and \[l=13cm\], to get the lateral area of the given cone. Hence, we will have the required areas of the cone.

Complete step-by-step solution:
According to the given question, we are given the radius and the slant height of a cone and we are asked to find the lateral area and the surface area of the cone.
Firstly, we will find the lateral area of the cone.
The formula for the lateral area of a cone, that we have is,
\[Lateral\_Area=\pi rl\]
We have, \[r=6cm\] and \[l=13cm\]

We will now substitute these values in the above formula and we get,
\[\Rightarrow \dfrac{22}{7}\times 6\times 13\]
Solving the above expression, we get,
\[\Rightarrow \dfrac{22}{7}\times 78\]
So, we have the value as,
\[\Rightarrow 245.1c{{m}^{2}}\]
Next, we will find the surface area of the cone and the formula for it that we have is,
\[Surface\_Area=\pi r\left( r+l \right)\]
Substituting the known values in the above equation, we get,
\[\Rightarrow \dfrac{22}{7}\times 6\times \left( 6+13 \right)\]
\[\Rightarrow \dfrac{132}{7}\times \left( 19 \right)\]
We have the value as,
\[\Rightarrow 358.3c{{m}^{2}}\]
Therefore, the lateral area of the cone is \[245.1c{{m}^{2}}\] and the surface area of the cone is \[358.3c{{m}^{2}}\].

Note: The formula of the lateral and surface area of the cone should be correctly known and written correctly as well. Also, while substituting the values in the formula, make sure that they are put correctly. We should always solve the expression in a stepwise manner to prevent any mistakes coming up. Also, the units are important, without the units, the answer is incomplete.