Question

A right triangle ABC with sides 8 cm , 15 cm and 17cm is revolved about the side 15 cm.Find the volume of the solid so obtained.​

Answer 1

Given :-

A right triangle ABC with sides 8 cm , 15 cm and 17cm is revolved about the side 15 cm.

To find :-

The volume of the solid so obtained.

Solution :-

Given that

∆ABC is a right angled triangle.

The sides of the triangle = 8 cm , 15 cm and

17 cm

The longest side = 17 cm

The hypotenuse = 17 cm

If we revolve the right angled triangle then the resultant solid is a cone.

Given that

The triangle is revolved about the side 15 cm

It will be the height of the solid.

Height of the cone (h) = 15 cm

Hypotenuse will be the slant height of the solid

Slant height of the cone (l) = 17 cm

The radius of the base of the cone (r) = 8 cm

We know that

Volume of a cone = (1/3)πr²h cubic units

Volume of the cone

=> V = (1/3)×(22/7)×(8)²×15 cm³

=> V = (1/3)×(22/7)×8×8×15 cm³

=> V = (22×8×8×15)/(3×7) cm³

=> V = (22×8×8×5)/7 cm³

=> V = 7040/7 cm³

=> V = 1005.71 cm³ (approximately)

Answer :-

The volume of the resultant solid (cone) is 7040/7 cm³ or 1005.71 cm³

Used formulae:-

♦ Volume of a cone = (1/3)πr²h cubic units

• r = radius
• h = height
• π = 22/7

Answer 2

Given:-

• Sides of right angle = 8cm,15cm and 17cm.
• It is revolved around side of 15 cm.

To find:-

• Volume of solid so obtained.

Solution:-

We will first draw a right-angled triangle (in attachment) and the we will revolve it around the side of 15cm(in attachment) . By doing so the figure which is obtained is a cone.

Hence, the dimension of cone are:-

• Diameter = 8cm
• Length = 17cm
• Height = 15cm

We know that the volume of cube is

$\large \green{\underline{ \blue{ \boxed{\bf{ \red{ \implies\frac{1}{3} {\pi r}^{2} h \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}}}}$

Where,

• π = 22/7 or 3.14
• r = radius
• h = height

As it is given that we have to use radius that's why we have to calculate radius first.

We know that:-

$\large \blue{\underline{ \green{ \boxed{\bf{ \red{ \implies\frac{d}{2} = r \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}}}}$

where,

• d = diameter
• r = radius

=>(1/3) ×(22/7) ×4²×15

=>(1/3) ×(22/7) ×16×15

=>(22/7) ×16×5

=>251.428

Hence, the volume of the solid formed by right angle triangle is (251.42cm³).