# Diameter of the base of the cone is $10.5cm$ and its slant height is $10cm$. Find its curved surface area.

A.$104.85c{m^2}$

B.$164.85c{m^2}$

C.$100.75c{m^2}$

D.None of these

Last updated date: 30th Mar 2023

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Answer

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Hint: Use the formula of curved surface area of cone & substitute the dimensions.

We know that the formula of curved surface area of the cone is $\pi rl$ where $r$ is radius of base of the cone and $l$ is slant height. In the given question we have given the diameter and we know the relation between radius and diameter which is $r = \dfrac{d}{2}$. On putting the values $r = \dfrac{d}{2} = \dfrac{{10.5}}{2} = 5.25cm$.Now we have got the radius so let’s put all the values in the formula

$\begin{gathered}

\pi rl \\

= 3.14 \times 5.25 \times 10 \\

= 3.14 \times 52.5 \\

= 164.85 \\

\end{gathered} $

Hence the required curved surface area is $164.85c{m^2}$.

Option B is correct.

Note: In mensuration formula is the key. If you know the formula and how to use it then you are done with the question. In the above question that’s what we have done. Know the formula and substitute in it correctly.

We know that the formula of curved surface area of the cone is $\pi rl$ where $r$ is radius of base of the cone and $l$ is slant height. In the given question we have given the diameter and we know the relation between radius and diameter which is $r = \dfrac{d}{2}$. On putting the values $r = \dfrac{d}{2} = \dfrac{{10.5}}{2} = 5.25cm$.Now we have got the radius so let’s put all the values in the formula

$\begin{gathered}

\pi rl \\

= 3.14 \times 5.25 \times 10 \\

= 3.14 \times 52.5 \\

= 164.85 \\

\end{gathered} $

Hence the required curved surface area is $164.85c{m^2}$.

Option B is correct.

Note: In mensuration formula is the key. If you know the formula and how to use it then you are done with the question. In the above question that’s what we have done. Know the formula and substitute in it correctly.

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