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

Answer

314.29 cm³ is the volume of the solid obtained.

Explanation

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

Let us assume that ∠B = 90°

[Refer the Attachment for figure]

Here; AB = 12 cm, BC = 5 cm and AC = 13 cm

After resolving the triangle about side 12 cm, we get

Radius (r) = 5 cm

Height (h) = 12 cm

We have to find the volume of the solid obtained. For that we have to find the volume of the solid.

We know that

Volume of cone = $\sf{\dfrac{1}{3}}$πr²h

Substitute the known values in above formula

$\implies\:\sf{\dfrac{1}{3}\:\times\:\dfrac{22}{7}\:\times\:(5)^2\:\times\:12}$

$\implies\:\sf{\dfrac{22}{21}\:\times\:25\:\times\:12}$

$\implies\:\sf{1.04762 \:\times\:300}$

$\implies\:\sf{314.28571\: cm^3}$

$\implies\:\sf{314.29\: cm^3}$ (approx.)

Answer 2

Question :--- A right triangle ABC with sides 5cm, 12cm and 13 cm is revolved about the side 12cm find the volume of the solid so obtained ?

Points Used :--

→ When a right ∆ is revolve around any sides to make a cone .

we have Three case :--

1) Revolve Around its Base :-

• Here, Radius of cone will become = Perpendicular Side of Right ∆.
• Height of cone = Base of Right ∆.

2) Revolve Around its Perpendicular Side :-

• Radius of cone = Base of Right ∆ .
• Height of cone = Perpendicular side of cone .

3) Revolve Around its Hypotenuse :--

• Here cone will be double .
• Height of cone = Hypotenuse of Right ∆.
• Radius of cone = ( Perpendicular * Base ) / Hypotenuse .

[ ओर हम इसको इस तरीके से आसानी से याद रख सकते है कि, जिस भी भुजा(side) से हम घुमाते है, वह भुजा हमारे cone की Height हो जाती है ll ]

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❁❁ Refer To Image First .. ❁❁

Solution :--

→ Right ∆ sides are given as 5, 12 and 13. and it revolves around side 12cm.

So, As told above , We can say that, (or we can see this in image . )

→ Height of cone = 12cm..

→ Radius of cone = 5cm.

Now, we have to Find volume of cone so formed.

☛ Volume of cone = 1/3 * π * (radius)² * Height

Putting values now , we get,

➠ Volume = 1/3 * π * (5)² * 12

➠ Volume = ( 25 * 3.14 * 4 )

➠ Volume = (100 * 3.14)

➠ Volume = (314)

➠ Volume = 314 cm³

Hence, Volume of Figure so obtained as cone is 314cm³ .