Question

the volume of a right circular cone is 9856cm2.if radius of the base is 14cm,find the height of the cone.​

Answer 1

$\bf{\underline{\underline \green{Solution:-}}}$

$\frak\red{AnswEr}\begin{cases}\sf\blue{\underline{The \: height \: of \: the \: cone = 48cm}}\end{cases}$

$\frak\red{Given}\begin{cases}\sf\red{\underline{Volume \: of \: right \:circular \: cone = 9856 cm^3}} \\ \sf\blue{\underline{Radius \: of \: the \: base = 14 cm}}\end{cases}$

$\frak\red{Need\:To\:Find}\begin{cases}\sf\pink{\underline{The \: height \: of \: the \: cone = \:?}}\end{cases}$

$\bf{\underline{\underline \green{ExPlanation:-}}}$

$\underline\mathtt \orange{Formula\:used\:here:-}$

$\bigstar\:\large{\boxed{\sf\pink{Volume \: of \: circular\: cone = \dfrac{1}{3}\pi r^2 h }}}$

$\underline\mathtt \orange{Now, Putting\:the\: values:-}$

$\longrightarrow \sf \green {9856 = \dfrac{1}{3}\times 3.14 \times (14)^2 \times Height}$

$\longrightarrow\sf \pink {9856 = \dfrac{1}{3}\times 3.14 \times 196 \times Height}$

$\longrightarrow\sf \red {9856 = \dfrac{615.44 \times Height}{3}}$ $\longrightarrow\sf \green {9856 = 205.147 \times Height}$ $\longrightarrow\sf\pink{ Height = \dfrac{\cancel{9856}}{\cancel{205.147}} }$

$\longrightarrow\sf \blue {Height = 48\:Cm}$

$\underline\mathtt \orange{ThereFore:}$

• $\small\orange{\underline {\boxed{\sf\green{ The \: height \: of \: the \: cone = 48cm} }}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Answer 2

ɢɪᴠᴇɴ :-

• Volume = 9856 cm³
• Radius (r) = 14 cm

ᴛᴏ ғɪɴᴅ :-

• Height (h)

sᴏʟᴜᴛɪᴏɴ :-

We know that,

$\implies \sf \: Volume \: of \: Cone = \frac{1}{3} \times \pi \times {r}^{2} \times h$

Put the above given values in it, we get,

$\implies \sf \: 9856 = \frac{1}{3} \times \frac{22}{7} \times {(14)}^{2} \times h \\ \\ \\ \implies \sf \: 9856 = \frac{1}{3} \times \frac{22}{7} \times 196 \times h \\ \\ \\ \implies \sf \: 9856 \times 3 = \frac{22 \times 196}{7} \times h\\ \\ \\ \implies \sf \: 29568 = 22 \times 28 \times h \\ \\ \\ \implies \sf \: h = \cancel\frac{29568}{616} \\ \\ \\ \implies \sf \: h = 48m$

Hence,

• Height (h) of cone = 48m