The quantities used to find area, length, width capacities and volume of things etc are called measures. Many countries have their own system of measures. But Metric System of measures is very simple and easy to calculate. The area is measured in square unit. In metric system the volume is measured in cubic units.
Example Problems - Metric Volume Units:
The triangular prism has width 6 cm, height 9 cm and length 11 cm. find the volume of triangular prism.
Solution:
Given:
Width (w) = 6 cm
Height (h) = 9 cm
Length (l) = 11 cm
Formula:
Volume of triangular prism (V) = `1/2` (l x w x h) cubic units
= `1/2` (11 x 6 x 9)
= `1/2` (594)
= 297
Volume of triangular prism (V) = 297 cm3
2. figure out the volume trapezoidal prism whose length 11 cm, height 8cm, length of parallel sides a=7 cm and b=4cm.
Solution:
Given:
Length (l) = 11cm
Height (h) = 8cm
Parallel sides a=7cm and b=4cm
Formula:
Volume of trapezoidal prism = l x area of the base cubic units
Area of the base:
Area of the base = `1/2` x (a + b) x h
= `1/2` x (7 + 4) x 8
=`1/2` x 11 x 8
= 44 cm2
Volume of trapezoidal prism = 11x 44
= 484
Volume of trapezoidal prism = 484 cm3
3. The cylinder has the radius r = 10 feet, h=23 feet. Find the volume of cylinder.
Solution:
Given:
r=10 cm
h=23 cm
Formula:
The volume of the cylinder = π x r2 x h cubic unit
=3.14 x (10)2 x 23
The volume of the cylinder = 7222 ft3.
Example Problems - Metric Volume Units:
Cone:
4. The cone has the radius = 10 feet and height = 23 feet. Find the volume of the cone.
Solution:
Given:
Radius (r) = 10 feet
Height (h) = 23 feet
Formula:
The volume of the cone =`1/3` x π x r2 x h
= `1/3` x 3.14 x (10)2 x 23
The volume of the cone = 2407.33 ft3
5. What is the volume rectangular prism with length 8 cm width 5 cm and height 6 cm?
Solution:
Given:
Length =8 cm
Width = 5 cm
Height = 6 cm
Formula:
Volume of rectangular solid (v) = l x w x h
= 8 x 5 x 6
= 240
Volume of rectangular solid (v) = 240 cm3
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