Question

A right angled triangle of which the sides containing the right angle are 6.3 cm and 10 cm in length, is made to turn round on the longer side. Find the volume of the solid, thus generated.

Answer 1

Hint: If a right angled triangle is rotated about the perpendicular, the solid that is generated is a cone and the cone that is generated has the height equal to the side about which the triangle is rotated and the other side forms the radius of the base of the formed cone.
Now, the volume of a cone can be calculated with the formula that is given as
\[=\dfrac{1}{3}\pi {{r}^{2}}h\]

Complete step-by-step answer:
As mentioned in the question, we have to find the volume of the cone that is generated when the right angled triangle is rotated about the side whose length is 10 cm.
Now, as the right angled triangle is rotated about the side with 10 cm, so, the height of the cone is 10 cm and the radius of the cone will become 6.3 cm.
Now, the volume of this generated cone can be calculated using the formula that is given in the hint as follows
\[\begin{align}
  & =\dfrac{1}{3}\pi {{\left( 6.3 \right)}^{2}}10 \\
 & =\dfrac{1}{3}\times 3.14\times {{\left( 6.3 \right)}^{2}}\times 10 \\
 & =4158\ c{{m}^{2}} \\
\end{align}\]
Hence, the volume of the generated solid which is a cone is 4158 sq. cm.

NOTE: - The students can make an error while finding the volume of the thus generated solid which is a cone if they don’t know about the fact that is given in the hint which states that if a right angled triangle is rotated about the perpendicular, the solid that is generated is a cone.
Also, the students can make an error if they don’t know about the important formulae that are mentioned in the hint as follows
The volume of a cone can be calculated with the formula that is given as
\[=\dfrac{1}{3}\pi {{r}^{2}}h\]