Question

What is the volume of aright circular cone of atitude 12cm & slant height 13cm given below

Answer 1

$\bigstar$ Question :

• What is the volume of a right circular cone of altitude 12 cm & slant height 13 cm .

$\bigstar$ Answer :

Given , In a right circular cone ,

Height , h = 12 cm , Slant Height , l = 13 cm

Now apply Pythagoras theorem for finding radius of cone.

⇒ r² + h² = l²

⇒ r² = 13² - 12²

⇒ r = √(169 - 144) = √25

⇒ r = 5 cm

Volume of the cone , $\bold{\bf{\red{V=\frac{1}{3}\pi r^2h}}}$

$\implies \bold{V=\frac{1}{3} \pi *5^2*12}\\\\\implies \bold{V=100\pi}\\\\\implies \bold{V=314\;cm^3}$

$\bold{\bf{\blue{Hence\;the\;volume\;of\;a\;right\;circular\;cone\;is\;314\;cm^3}}}$

Answer 2

$\large\bf\underline{Given:-}$

• Altitude of cone = 12cm
• Slent height = 13cm

$\large\bf\underline {To \: find:-}$

• Volume of cone.

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

We know that,

$\large\bf \blacktriangleright \: l = \sqrt{ {r}^{2} + {h}^{2} }$

$\dashrightarrow \rm 13 = \sqrt{ {r}^{2} + 12 {}^{2} } \\ \\ \dashrightarrow \rm \:13 = \sqrt{ {r}^{2} + 144 } \\ \\ \dashrightarrow \rm \: {13}^{2} = {r}^{2} + 144 \\ \\ \dashrightarrow \rm \:169 - 144 = {r}^{2} \\ \\ \dashrightarrow \rm \:25 = {r}^{2} \\ \\ \dashrightarrow \rm \:r = \sqrt{25} \\ \\ \dashrightarrow \bf \: r = 5cm$

$\large\blacktriangleright \bf \: volumeof \: cone \: = \frac{1}{3} \pi \: r {}^{2} h \\ \\ \longrightarrow \rm \: volume \: of \: cone \: = \frac{1}{3} \times \frac{22}{7} \times {5}^{2} \times 12 \\ \\ \longrightarrow \rm \: volume \: of \: cone \: = \frac{22}{7} \times 25 \times 4 \\ \\ \longrightarrow \rm \: volume \: of \: cone \: = 314.28cm^3 \:$