Question

Write the volume of a right circular cylinder of base radius 7 cm and height 10 cm.

Answer 1

Hint:
Here, we need to find the volume of the given right circular cylinder. We will use the formula for the volume of a right circular cylinder, and the given information to calculate the required volume. Cylinder is a three dimensional geometric shape which has two circular bases at a certain distance and are joined by a curved surface.

Formula used:
The volume of a right circular cylinder is given by the formula \[\pi {r^2}h\], where \[r\] is the radius of the base, and \[h\] is the height of the right circular cylinder.

Complete Step by Step Solution:
It is given that the radius of the base of the right circular cylinder is 7 cm.
Thus, we get
Radius of the base \[ = r = 7\] cm.
It is given that the height of the right circular cylinder is 7 cm.
Thus, we get
Height of the cylinder \[ = h = 10\] cm.
Now, we need to find out the volume of the right circular cylinder.
Substituting \[r = 7\] cm and \[h = 10\] cm in the formula Volume of cylinder \[ = \pi {r^2}h\], we get
Volume of the right circular cylinder \[ = \pi {\left( 7 \right)^2}{\rm{10 c}}{{\rm{m}}^3}\]
Applying the exponent on the base, we get
\[ \Rightarrow \] Volume of the right circular cylinder \[ = \pi \left( {49} \right){\rm{10 c}}{{\rm{m}}^3}\]
Multiplying the terms in the expression, we get
\[ \Rightarrow \] Volume of the right circular cylinder \[ = 490\pi {\rm{ c}}{{\rm{m}}^3}\]
Substituting \[\pi = \dfrac{{22}}{7}\] in the expression, we get
\[ \Rightarrow \] Volume of the right circular cylinder \[ = 490 \times \dfrac{{22}}{7}{\rm{ c}}{{\rm{m}}^3}\]
Simplifying the expression, we get
\[ \Rightarrow \] Volume of the right circular cylinder \[ = 70 \times 22{\rm{ c}}{{\rm{m}}^3}\]
Multiplying the terms in the expression, we get
\[ \Rightarrow \] Volume of the right circular cylinder \[ = 1540{\rm{ c}}{{\rm{m}}^3}\]

Therefore, we get the volume of the given right circular cylinder as 1540 \[{\rm{c}}{{\rm{m}}^3}\].

Note:
We substituted \[\pi = \dfrac{{22}}{7}\] in the solution. The value of \[\pi \] can be taken as either \[\pi = \dfrac{{22}}{7}\] or \[\pi = 3.14\].
Substituting \[\pi = 3.14\] in the solution, we get the volume as
Volume of the right circular cylinder \[ = 490 \times 3.14{\rm{ c}}{{\rm{m}}^3} = 1538.6{\rm{ c}}{{\rm{m}}^3}\]
Therefore, we get the volume of the given right circular cylinder as \[1538.6\]\[{\rm{c}}{{\rm{m}}^3}\]. This is almost equal to the value 1540 \[{\rm{c}}{{\rm{m}}^3}\] obtained by substituting \[\pi = \dfrac{{22}}{7}\].