Question

a right triangle ABC with sides 5cm, 12cm , and 13cm is revolved about the side 12cm . Find the volume of the solid so obtained.​

Answer 1

$\underline{\underline{\red{Answer}}}$

$\underline{\underline{\mathbb{EXPLANATION}}}$

$\rm{\pink{When\:we\:rotate\:a\:right\:angled\:Trangle\;having\:axis\:of\:rotation}}$

$\rm{\pink{perpendicular\:And\:radius\:equal\:to\:base\:then\:the\:solid\:so\:formed\:is\:Cone.}}$

$\underline{\underline{\boxed{\pink{\rm{Volume\:Of\:Cone=\frac{1}{3}\pi\:r^2h}}}}}$

$\rm{\red{here\:r=5cm,\:h=12cm}}$

$\implies{\rm{volume\:of\:cone\:=\frac{1}{3}\pi\:\left(5\right)^2\left(12\right)}}$

$\implies{\rm{volume\:of\:cone\:=\frac{1}{3}\left(3.14\right)\left(5\right)^2\left(12\right)}}$

$\implies{\rm{volume\:of\:cone\:=\frac{1}{3}\left(3.14\right)\left(25\right)\left(12\right)}}$

$\therefore{\rm{volume\:of\:cone\:=314.28cm^3}}$

Answer 2

» A right triangle ABC with sides 5cm, 12cm , and 13cm is revolved about the side 12cm.

• Let $\angle{B}$ = 90°

[Refer the Attachment for figure]

Here..

AB = 12 cm

BC = 5 cm

AC = 13 cm

• After resolving the triangle about side 12 cm.. we get

Radius (r) = 5 cm

Height (h) = 12 cm

_______________ [GIVEN]

• We have to find the volume of the solid obtained.

_________________________________

We know that ..

Volume of cone = $\dfrac{1}{3}$ πr²h

=> $\dfrac{1}{3}$ × $\dfrac{22}{7}$ × (5)² × 12

=> $\dfrac{22}{21}$ × 25 × 12

=> 1.04762 × 300

=> 314.28571 cm³

=> 314.29 cm³ (approx.)

_______________________________

Volume of the solid is 314.29 cm³

____________ [ANSWER]

_______________________________