Solving Geometric Volumes
Volume is the amount of space enclosed by a shape or object
, how much 3-dimensional space (length, width, and height) it occupies. Volumes of straight-edged, circular shape, regular, and can be simply calculated using formulas. Integral calculus is used to find the more complicated shapes if a formula exists for its boundary. In geometric volumes consist of volume of cube, Rectangular prism, cylinder.
Following are the problems given for solving geometric volumes:
Solving Geometric Volumes for Different Shapes:
Formula for solving geometric volumes of the cube = a^3.
a = side length of the cube.
Example Problems:
1. The side length of cube is 4 meters. Find the volume of the cube.
Solution:
Volume of the cube =a^3.
a = 4 meters.
= (4)^3.
Volume of the cube =64 m^3.
2. The side length of cube is 7 meters. Find the geometric volumes of the cube.
Solution:
Volume of the cube = a^3.
a = 7 meters.
= (8)^3.
Volume of the cube =343 m^3.
Rectangular prism:
Formula for geometric volumes of the rectangle = a x b x c.
a, b, c are the side (length) duration of rectangular prism.
Problem:
1. The side lengths of the rectangular prisms are 2 cm, 3cm, and 4cm respectively. Find the volume.
Solution:
Volume of the rectangular prism= a x b x c
a= 2 cm
b= 3 cm
c= 4 cm
= 2 x 3 x 4
Volume of the rectangular prism = 24 cm^3.
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2. The side lengths of the rectangular prisms are 5 cm, 6cm, and 8cm respectively. Find the geometric volumes.
Solution:
Volume of the rectangular prism= a x b x c
a = 5cm
b = 6cm
c = 8cm
= 4 x 7 x 9
Volume of the rectangular prism = 240 cm^3.
Solving Geometric Volumes for Cylinder:
Volume of the cylinder = r^2h
r = radius.
h = height.
Example problem for solving geometric volumes:
The radius and height of cylinder are 5 inches and 7 inches respectively. Find the geometric volumes of cylinder.
Solution:
Volume of the cylinder = r^2h.
r = 5 inches
h = 7 inches
= 3.14 x 5 x 7
=109.9 in^3.
2.The radius and height of cylinder are 4 inches and 8 inches respectively. Find the geometric volumes of cylinder.
Solution:
Volume of the cylinder = r^2h.
r =4 inches
h= 8 inches
= 3.14 x 4 x 8
=100.48 in^3.
by: nitinp
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