Question

The diameter of the base of right circular none is $10m$ and its height is $12m$ , then the total surface is
$\begin{align}
  & \left( A \right)250 < S < 300 \\
 & \left( B \right)200 \\
 & \left( C \right)S=270 \\
 & \left( D \right)S>30 \\
\end{align}$

Answer 1

Hint: From the question given that the diameter of the base of right circular none is $10m$ and its height is $12m$, we have to find the total surface area of the right circular none. As we know that the formula for the total surface area of the right circular none is $\pi r\left( r+l \right)$, where r is the radius and “l” is the slant height of the right circular none. As we know that radius is half of the diameter by this we will get the radius and we also know that the value of “l” will be equal to the $\sqrt{{{r}^{2}}+{{h}^{2}}}$.

Complete step by step solution:
From the question given that the diameter of circular none is,
$\Rightarrow d=10m$
As we know that radius is half of the diameter,
Therefore, the radius will be,
$\Rightarrow r=\dfrac{d}{2}=\dfrac{10}{2}=5m$
$\Rightarrow r=5m$
And also given that the height of the right circular none is,
$\Rightarrow h=12m$
As we know that the slope height that is the value of “l” is equal to the
$\Rightarrow l=\sqrt{{{r}^{2}}+{{h}^{2}}}$
From this we will get the value of “l”, the value we will get is,
$\Rightarrow l=\sqrt{{{5}^{2}}+{{12}^{2}}}$
$\Rightarrow l=\sqrt{25+144}$
$\Rightarrow l=\sqrt{169}$
$\Rightarrow l=13$
As we know that the total surface area of the right circular none is equal to the
$\Rightarrow T.S.A=\pi r\left( r+l \right)$
Now we have to substitute the respective values in their positions,
By substituting we will get,
$\Rightarrow T.S.A=\pi r\left( r+l \right)$
$\Rightarrow T.S.A=\pi \times 5\left( 5+13 \right)$
$\Rightarrow T.S.A=\pi \times 5\times 18$
$\Rightarrow T.S.A=\pi \times 90$
$\Rightarrow T.S.A=3.14\times 90$
$\Rightarrow T.S.A=282.6$
Therefore, the option will be $\left( A \right)250 < S < 300$ because $282.6$lies between the $250$ and $300$.
the figure will be as follows.

Note: students should also know the formulas like, Curved surface area of right circular cone is $\pi rl$. Volume of the right circular cone is $\dfrac{1}{3}\pi {{r}^{2}}h$, students should also note that the in the given options, option $\left( D \right)S>30$ is also correct when this question belongs to multiple options correct, but here the question belongs to single correct answer so we should not write option $\left( D \right)S>30$.