Question

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

Answer 1

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Answer 2

Answer:

Given :-

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

Find Out :-

• What is the volume of the solid so obtained.

Formula Used :-

$\bigstar$ Volume Of Cone Formula :

$\longrightarrow \sf\boxed{\bold{\pink{Volume_{(Cone)} =\: \dfrac{1}{3}{\pi}r^2h}}}$

where,

• π = Pie or 22/7
• r = Radius
• h = Height

Solution :-

Given :

• Radius of cone = 5 cm
• Height of cone = 12 cm

According to the question by using the formula we get,

$\dashrightarrow \sf Volume_{(Cone)} =\: \dfrac{1}{3} \times \dfrac{22}{7} \times (5)^2 \times 12$

$\dashrightarrow \sf Volume_{(Cone)} =\: \dfrac{1}{3} \times \dfrac{22}{7} \times (5 \times 5) \times 12$

$\dashrightarrow \sf Volume_{(Cone)} =\: \dfrac{1 \times 22}{3 \times 7} \times (25) \times 12$

$\dashrightarrow \sf Volume_{(Cone)} =\: \dfrac{22}{21} \times 300$

$\dashrightarrow \sf Volume_{(Cone)} =\: \dfrac{22 \times 300}{21}$

$\dashrightarrow \sf Volume_{(Cone)} =\: \dfrac{6600}{21}$

$\dashrightarrow \sf Volume_{(Cone)} =\: 314.29$

$\dashrightarrow \sf\bold{\red{Volume_{(Cone)} \approx\: 314\: cm^3}}$

$\therefore$ The volume of the solid so obtained is 314 cm³ .

[Note :- Please refer the attachment for the diagram of this question. ]