Question

Find the volume of the cylinder if height (h) and radius of the base (r) are given as:
A) \[r=10.5\text{ }cm,\text{ }h=8\text{ }cm\]
B) \[r=2.5\text{ }cm,\text{ }h=7\text{ }cm\]
C) \[r=4.2\text{ }cm,\text{ }h=5\text{ }cm\]
D) \[r=5.6\text{ }cm,\text{ }h=5\text{ }cm\]

Answer 1

Hint: To find the volume of the cylinder we multiply the product of the area of the circle of the cylinder with the height of the cylinder. The formula for the volume of the cylinder is
Volume of the cylindrical container \[=\pi {{r}^{2}}h\]
where \[r\] is the radius of the cylinder in centimeters and \[h\] is the height of the cylinder in centimeters and \[\pi =3.14\].

Complete step-by-step answer:
A) For \[r=10.5\text{ }cm,\text{ }h=8\text{ }cm\]
Placing the values of the radius and height in the formula we get:
 Volume of the cylindrical container \[=\pi {{r}^{2}}h\]
\[=\pi \times {{\left( 10.5 \right)}^{2}}\times 8\]
\[=2769.48\text{ }c{{m}^{3}}\]
B) For \[r=2.5\text{ }cm,\text{ }h=7\text{ }cm\]
Placing the values of the radius and height in the formula we get:
 Volume of the cylindrical container \[=\pi {{r}^{2}}h\]
\[=\pi \times {{\left( 2.5 \right)}^{2}}\times 7\]
\[=137.44\text{ }c{{m}^{3}}\]
C) \[r=4.2\text{ }cm,\text{ }h=5\text{ }cm\]
Placing the values of the radius and height in the formula we get:
 Volume of the cylindrical container \[=\pi {{r}^{2}}h\]
\[=\pi \times {{\left( 4.5 \right)}^{2}}\times 5\]
\[=318.08\text{ }c{{m}^{3}}\]
D) \[r=5.6\text{ }cm,\text{ }h=5\text{ }cm\]
Placing the values of the radius and height in the formula we get:
 Volume of the cylindrical container \[=\pi {{r}^{2}}h\]
\[=\pi \times {{\left( 5.6 \right)}^{2}}\times 5\]
\[=492.60\text{ }c{{m}^{3}}\]

Note: For instance, if we were asked to find the curved surface area of the cylinder then we would use the formula as Curved surface area \[=2\pi rh\]. For total surface area we would have use the curved surface area and also the area of the two circles top and bottom as Total surface area \[=2\pi rh+2\pi {{r}^{2}}\] where \[r\] and \[h\] are the radius and height of the cylinder. So apart from volume these are two other measuring functions of a cylinder.