Question

If the volume of right Circular Cone is 48cm³ and height 9cm then, find diameter of base .​

Answer 1

Correct Question :-

• If the volume of right Circular Cone is 48pi cm³ and height 9cm then, find diameter of base .

Given :-

• Height of the Cone = 9cm
• Volume of the Cone = 48$\pi {cm}^{3}$

To Find :-

• Diameter of the Base of the Cone.

Solution :-

Firstly we will find the Radius of the Cone then we can easily find the Diameter.

$\quad {:} \longrightarrow \sf \boxed{\bf{Volume \: of \: Cone \: = \: \dfrac{1}{3}\pi \: {r}^{2} \: h }}$

$\longmapsto \sf {\sf{48 \cancel{\pi} \: = \: \dfrac{1}{ \cancel3} \cancel\pi \: {r}^{2} \: \cancel9 }}$

$\longmapsto \sf {\sf{48 \: = \: 3 \: {r}^{2} \: }}$

$\longmapsto \sf {\sf{ \cancel\dfrac{48}{3} \: = \: \: {r}^{2} \: }}$

$\longmapsto \sf {\sf{ 16 \: = \: \: {r}^{2} \: }}$

$\longmapsto \sf {\sf{ \sqrt{16} \: = \: \: r \: }}$

$\longmapsto \sf {\bf{ 4 \: = \: \: Radius \: }}$

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We Know that ,

• Diameter is Double of Radius.

$\qquad \quad {:} \longrightarrow \sf \boxed{\sf{Diameter \: = \: 2 \: \times \: Radius }}$

$\qquad \quad {:} \longrightarrow \sf {\tt{Diameter \: = \: 2 \: \times \: 4}}$

$\qquad \quad {:} \longrightarrow \sf {\bf{Diameter \: = \: 8cm}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Diameter \: of \: Cone \: = \underline {\underline{ 8cm}}}\\\end{gathered}\end{gathered}$

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More For Knowledge :-

$\boxed{\begin{minipage}{6 cm}\bigstar \:\underline{\textbf{Formulae Related to Cone :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area\:of\:Base + CSA=\pi r^2+\pi rl\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\dfrac{1}{3}\pi r^2h\\ \\{\textcircled{\footnotesize\textsf{5}}} \: \:Slant \: Height=\sqrt{r^2 + h^2}\end{minipage}}$

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