Question

a cone has base radius 5cm and perpendicular height 9cm. work out the volume of the cone

Answer 1

Required Answer :

The volume of cone = 235.71 cm³

Given :

• Radius of a cone = 5 cm
• Perpendicular height of the cone = 9 cm

To find :

• Volume of the cone

Solution :

Here, in this question we are given the radius and height of a cone and we need to calculate the volume of the cone. So, for that we will directly apply the values in the formula of volume of cone.

Formula to calculate the volume of cone :

• Volume of cone = 1/3 πr²h

where,

• Take π = 22/7
• r denotes the radius of the cone
• h denotes the height of the cone

we have,

• r = 5 cm
• h = 9 cm

Substituting the given values :

⇒ Volume of the cone = 1/3 × 22/7 × (5)² × 9

⇒ Volume of the cone = 1/3 × 22/7 × 25 × 9

⇒ Volume of the cone = 22/7 × 25 × 3

⇒ Volume of the cone = 1650/7

⇒ Volume of the cone ≈ 235.71

Therefore, the volume of cone = 235.71 cm³

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Some related formulae :

• Surface area of sphere = 4πr²
• Volume of cylinder = πr²h
• Curved surface area of cone = πrl
• Total surface area of cone = πr(r + l)
• Total surface area of cylinder = 2πrh + 2πr²

where,

• Take π = 22/7
• r = radius
• h = height
• l = slant height

Answer 2

Answer:

${\Large{\pmb{\sf{\underline{\underline{Given...}}}}}}$

• $\leadsto$ Radius of Cone = 5 cm
• $\leadsto$ Perpendicular height of Cone = 9 cm

$\begin{gathered}\end{gathered}$

${\Large{\pmb{\sf{\underline{\underline{To \: Find...}}}}}}$

• $\leadsto$ Volume of Cone

$\begin{gathered}\end{gathered}$

${\Large{\pmb{\sf{\underline{\underline{Using \: Formula...}}}}}}$

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

Where:

• $\dashrightarrow$ $\pi$ = 22/7
• $\dashrightarrow$ r = radius of cone
• $\dashrightarrow$ h = height of cone

$\begin{gathered}\end{gathered}$

${\Large{\pmb{\sf{\underline{\underline{Diagram...}}}}}}$

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{5 cm}}\put(9.5,10){\sf{9 cm}}\end{picture}$

• Request : See the diagram of from website Brainly.in..
• Check Out the given attachment also.

$\begin{gathered}\end{gathered}$

${\Large{\pmb{\sf{\underline{\underline{Solution...}}}}}}$

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

• Substituting the values

$\quad{\longmapsto{\sf{Volume \: of \: Cone = \dfrac{1}{3} \times {\dfrac{22}{7}} \times {5}^{2} \times 9}}}$

$\quad{\longmapsto{\sf{Volume \: of \: Cone = \dfrac{1}{3} \times {\dfrac{22}{7}} \times {5 \times 5}\times 9}}}$

$\quad{\longmapsto{\sf{Volume \: of \: Cone = \dfrac{1}{\cancel{3}} \times {\dfrac{22}{7}} \times {5 \times 5}\times \cancel{9}}}}$

$\quad{\longmapsto{\sf{Volume \: of \: Cone = {\dfrac{22}{7}} \times {5 \times 5}\times 3}}}$

$\quad{\longmapsto{\sf{Volume \: of \: Cone = {\dfrac{22 \times 25 \times 3}{7}}}}}$

$\quad{\longmapsto{\sf{Volume \: of \: Cone = {\dfrac{1650}{7}}}}}$

$\quad{\longmapsto{\sf{Volume \: of \: Cone \approx {235.71 \: {cm}^{3}}}}}$

$\quad{\dag{\underline{\boxed{\sf{\purple{Volume \: of \: Cone \approx {235.71 \: {cm}^{3}}}}}}}}$

${\therefore{\sf{\underline{\underline{\red{The \: Volume \: of \: Cone \: is \: 235.71 \: {cm}^{3}..}}}}}}$

$\begin{gathered}\end{gathered}$

${\Large{\pmb{\sf{\underline{\underline{Learn \: More...}}}}}}$

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