Question

if the volume of right Circular Cone height 9cm is 48 pi cm3 find diameter of base .
Class 9
13 chapter please fast answer.​

Answer 1

Given :

• Height of Cone is 9 cm .
• Volume of Cone is 48 π cm³ .

To Find :

• Diameter of Base .

Solution :

Firstly we will find the Radius of Cone :

Using Formula :

$\longmapsto\tt\boxed{Volume\:of\:Cone=\dfrac{1}{3}\pi{{r}^{2}h}}$

Putting Values :

$\longmapsto\tt{48\:{\cancel{\pi}}=\dfrac{1}{{\not{3}}}{\cancel{\pi}}\times{{r}^{2}}\times{{\not{9}}}}$

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

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

$\longmapsto\tt{\sqrt{16}=r}$

$\longmapsto\tt\bf{4\:cm=r}$

So , The Radius of Cone is 4 cm .

Now ,

As we know that Diameter is double of Radius . So ,

$\longmapsto\tt{2r}$

$\longmapsto\tt{2(4)}$

$\longmapsto\tt\bf{8\:cm}$

So , The Diameter of Cone is 8 cm .

Answer 2

Answer:

$\setlength{\unitlength}{7mm}\begin{picture}(6, 4)\linethickness{0.26mm}</p><p>\qbezier(5.8,2.0)(5.8,2.3728)(4.9799,2.6364)\qbezier(4.9799,2.6364)(4.1598,2.9)(3.0,2.9)\qbezier(3.0,2.9)(1.8402,2.9)(1.0201,2.6364)\qbezier(1.0201,2.6364)(0.2,2.3728)(0.2,2.0)\qbezier(0.2,2.0)(0.2,1.6272)(1.0201,1.3636)\qbezier(1.0201,1.3636)(1.8402,1.1)(3.0,1.1)\qbezier(3.0,1.1)(4.1598,1.1)(4.9799,1.3636)\qbezier(4.9799,1.3636)(5.8,1.6272)(5.8,2.0)\put(0.2,2){\line(1,0){2.8}}\put(3.2,4){\sf{9 cm}}\put(3,2){\line(0,2){4.5}}\put(1.4,1.6){\sf{Volume = 48 \pi }}\qbezier(.185,2.05)(.7,3)(3,6.5)\qbezier(5.8,2.05)(5.3,3)(3,6.5)\put(3,2.02){\circle*{0.15}}\put(2.7,2){\dashbox{0.01}(.3,.3)}\end{picture}$

• Volume of cone = 48π
• Height = 9 cm
• Diameter of Base = ?

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\Longrightarrow\sf Volume=\dfrac{1}{3}\pi r^2h\\\\\\:\Longrightarrow\sf 48\pi=\dfrac{1}{3}\pi r^2 \times 9\\\\\\:\Longrightarrow\sf 48\pi \times 3 \times \dfrac{1}{\pi \times 9} =r^2\\\\\\:\Longrightarrow\sf 16=r^2\\\\\\:\Longrightarrow\sf \sqrt{16} = r\\\\\\:\Longrightarrow\sf r = 4 \:cm$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{Diameter of the base of cone :}}$

$:\Longrightarrow\sf Diameter=2 \times Radius\\\\\\:\Longrightarrow\sf Diameter=2 \times 4\:cm\\\\\\:\Longrightarrow\sf Diameter=8\:cm$

⠀

$\therefore\:\underline{\textsf{Diameter of the base of cone is \textbf{8 cm}}}.$