Question

What is the volume of a right triangle ?

Answer 1

Hint: We have to find the volume of a right angled triangle . We stated the definition of the right triangle , what is the volume of a given object , and the formula for the volume of the right triangle . We will also discuss its shape . And Also the steps on how to calculate the formula and the shape .

Complete step-by-step answer:
Definition of right triangle :
It is the type of triangle in which one the three angles is a right angled triangle I.e. 90 degree. The longest side of the triangle is called the hypotenuse of the triangle . The other two sides are called the base and perpendicular side; the point above the right angle is called the perpendicular and the point which lies on the base I.e. parallel to the point of right angle .

What is volume ?
Volume is defined as the measurement of the amount of space which is occupied by the object or a shape . The measurement of volume differs from shape to shape and object to object . Volume is a three dimensional \[\left( {{\text{ }}3{\text{ }} - {\text{ }}D{\text{ }}} \right)\] quantity . It has three dimensions: height , width and length of the object .
Shape of right triangle :
The diagram of the required shape is stated as a right angled prism . We can’t find the volume of \[2 - D\] objects , so to find the volume of a right angled triangle it forms a shape like that of a prism .
As we know the area of a right angled triangle \[ = {\text{ }}\left( {\dfrac{1}{2}} \right){\text{ }} \times {\text{ }}base{\text{ }} \times {\text{ }}height\]
For finding the volume of an object the volume is equal to the area into the width of the right triangle .
Hence , the formula of volume of right triangle
Volume of right triangle \[\left( {{\text{ }}V{\text{ }}} \right){\text{ }} = {\text{ }}\left( {\dfrac{1}{2}} \right){\text{ }} \times {\text{ }}base{\text{ }} \times {\text{ }}height{\text{ }} \times {\text{ }}width\]
Let \[base{\text{ }} = {\text{ }}b{\text{ }},{\text{ }}height{\text{ }} = {\text{ }}h\]and \[width{\text{ }} = {\text{ }}l\]
So , the formula becomes
\[V{\text{ }} = {\text{ }}\left( {\dfrac{1}{2}} \right){\text{ }} \times {\text{ }}b{\text{ }} \times {\text{ }}h{\text{ }} \times {\text{ }}l\;\]
Hence , the volume of volume of right triangle \[ = {\text{ }}\left( {\dfrac{1}{2}} \right){\text{ }} \times {\text{ }}b{\text{ }} \times {\text{ }}h{\text{ }} \times {\text{ }}l\]

Note: Formula of volume :
Various formulas are given below :
Volume of sphere $ = (\dfrac{4}{3}) \times \pi \times {r^3}$
Volume of hemisphere $ = (\dfrac{2}{3}) \times \pi \times {r^3}$
Volume of cone $ = \pi \times {r^2} \times (h/3)$
Volume of cylinder $ = \pi \times {r^2} \times h$
Where $r$ is the radius and $h$ is the height go the object