Question

$\large {\dag \; {\underline{\underline{\red{\pmb{\textbf{\textsf{ \; Question \; :- }}}}}}}}$

$\longmapsto$ The height and the slant height of a cone are 21 cm and 28 cm respectively . Find :-



◕ Radius of the Cone
◕ Volume of the Cone


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$\green{\textsf{ Thanks in Advance :D }}$​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Slant height of cone, l = 28 cm

Height of cone, h = 21 cm

Let assume that radius of cone = r cm

We know, slant height (l), height (h) and radius (r) of a cone are interrelated by the relationship

$\rm \: {l}^{2} = {r}^{2} + {h}^{2}$

$\rm \: {28}^{2} = {r}^{2} + {21}^{2}$

$\rm \: 784 = {r}^{2} + 441$

$\rm \: {r}^{2} = 784 - 441$

$\rm \: {r}^{2} = 343$

$\rm \: r = \sqrt{343}$

$\rm \: r \: = \: \sqrt{7 \times 7 \times 7}$

$\color{green}\rm\implies \:\boxed{ \rm{ \:r \: = \: 7 \sqrt{7} \: cm \: }}$

Now, We know volume of cone of radius r and height h is given by

$\boxed{ \rm{ \:Volume_{(cone)} \: = \: \frac{1}{3} \times \pi \: {r}^{2} \: h \: }}$

So, on substituting the values, we get

$\rm \: Volume_{(cone)} \: = \: \dfrac{1}{3} \times \dfrac{22}{7} \times 7 \sqrt{7} \times 7 \sqrt{7} \times 21$

$\rm \: Volume_{(cone)} = 22 \times 7 \times 7 \times 7$

$\color{green}\rm\implies \:\boxed{ \rm{ \:Volume_{(cone)} \: = \: 7546 \: {cm}^{3} \: }}$

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Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Answer:

Given that :-

• Height of Cone is 21 cm.
• Slant Height of Cone is 28 cm.

To find :-

• Radius and Volume of Cone?

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Solution:-

Height ( h ) = 21cm

Slant Height ( l ) = 28 cm

»» I By Pythagoras theorem

(slant height)² =(radius)²+(height)²

»» r² = l² - h²

r² = (28)² - (21)²

=> √ 784 - 441

=> √ 343

=> r = 7 √ 7

Therefore, Radius of Cone is 7√7 cm

$Volume = \frac{1}{3} (\pi {r}^{2}h)$

=> { (22/7) × 343 × 21 } / 3

=> 7546

$Therefore, Volume \: of \: Cone \: is \: 7546cm³$

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