Question

5. A right triangle of sides 5cm, 12cm and 13cm is revolved about the side 5cm.find the
volume of the solid so generated.

Answer 1

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Given:

In a right angled triangle,

Sides are 5 cm, 12 cm, 13 cm and is

revolved about the side 5 cm

To find:

Volume of solid cone generated by revolving = ?

Explanation:

Refer attachment for more information

In right angled triangle,

Hypotenuse = 13 cm

Height = 5 cm

Adjacent side = 12 cm

After revolution,

There is formation of solid cone,

Height = h = 5 cm

Radius = r = 12 cm

$\\ \\ Volume \: of \: cone \: = \dfrac{1}{3} \pi \: r {}^{2} h \\ \\ = \dfrac{1}{3} \pi \times (12) {}^{2} \times 5 \\ \\ = \dfrac{1}{3} \pi \times 144 \times 5$

$\\ \\ = \dfrac{1}{3} \times \pi \times 720 \\ \\ = 240\pi \\ \\ = 754 \: cm {}^{3}$

Answer:

Therefore, volume of solid cone formed is 240π or 753 cm³

Knowledge booster:

1. Value of π is 22/7 or 3.14
2. Hypotenuse is the longest side of the right angle triangle and it is opposite to 90°
3. Try solving more such questions to get good hold on it