VOLUME OF 3D SHAPES

About "Volume of 3d shapes"

Volume of 3d shapes :

Here, we are going to see, how to calculate volume of 3-D shapes such as cubes, cuboids, prisms and pyramids.

When we are trying to find volume of a 3-D shape, we have to consider the following important points. 

1. Let the base of a prism be a rectangle or square. If all the side walls are either rectangles or squares (that is, no side wall is triangle), then prism will look like as given below. 

The formula to find volume of the above prism 

=  Base area x Height

2. Let the base of a prism be a rectangle or square. If two of the side walls side walls are triangles and other two side walls are rectangles or squares, then prism will look like as given below. 

The formula to find volume of the above prism 

=  (1/2) x Base area x Height

3. Let the base of a prism be a triangle. If all of the side walls are rectangles or squares, then the prism will look like as given below.  

The formula to find volume of the above prism 

=  Base area x Height

4. Let the base of a prism be a rectangle or square or triangle. If all of the side walls are triangles, then the prism will be a pyramid and it will look like as given below. 

The formula to find volume of the above pyramid 

=  (1/3) x Base area x Height

Volume of 3d shapes - Practice problems

Problem 1 : 

Find the volume-of the cuboid given below.

Solution : 

Here, the base is  a rectangle and all the side walls are also rectangles. 

Then, we have

Volume-of the cuboid   =  Base area x Height

Here, the base is a rectangle with length 12 cm and width 4 cm. 

Area of base  =  12 x 4  =  48 sq. cm

Height of the cuboid  =  8 cm

Volume-of cuboid   =  48 x 8

Volume-of cuboid   =  384 cubic cm

Problem 2 : 

Find the volume-of the cube given below.

Solution : 

Here, the base is  a square and all the side walls are also squares. 

Then, we have

Volume-of the cube   =  Base area x Height

Here, the base is a square with side length of 8 cm.  

Area of base  =  8 x 8  =  64 sq. cm

Height of the cube  =  8 cm

Volume-of cube  =  64 x 8

Volume-of cuboid   =  512 cubic cm

Problem 3 : 

Find the volume-of the triangular prism given below.

Solution : 

Here, the base is  a rectangle, two of the side walls are triangles and other two side walls are rectangles. 

Then, we have

Volume-of the prism   =  (1/2) x Base area x Height

Here, the base is a rectangle with length 7 cm and width is 4 cm.

So, area of the base  =  7 x 4  =  28  sq. cm

Height of the prism  =  3 cm

Volume-of the prism  =  (1/2) x 28 x 3

Volume-of the prism  =  42 cubic cm

Problem 4 : 

Find the volume-of the triangular prism given below.

Solution : 

Here, the base is  a rectangle, two of the side walls are triangles and other two side walls are rectangles. 

Then, we have

Volume-of the prism   =  (1/2) x Base area x Height

Here, the base is a rectangle with length 12 cm and width is 8 cm.

So, area of the base  =  12 x 8  =  96 sq. cm  

Height of the prism  =  3 cm

Volume-of the prism  =  (1/2) x 96 x 3

Volume-of the prism  =  144 cubic cm

Problem 5 : 

Find the volume-of the triangular prism given below.

Solution : 

Here, the base is  a triangle, and all the side walls are rectangles.

Then, we have

Volume-of the prism   =  Base area x Height

Here, the base is a triangle with base 6 cm and height 4 cm. 

So, area of the base  =  (1/2) x 6 x 4  =  12 sq. cm  

Height of the prism  =  8 cm

Volume-of the prism  =  12 x 8

Volume-of the prism  =  96 cubic cm

Problem 6 : 

Find the volume-of the pyramid given below.

Solution : 

Volume-of the pyramid   =  (1/3) x Base area x Height

Here, the base is a square with side length 8 cm. 

So, area of the base  =  8 x 8  =  64 sq. cm  

Height of the pyramid  =  9 cm

Volume-of the pyramid  =  (1/3) x 64 x 9

Volume-of the prism  =  192 cubic cm

After having gone through the stuff given above, we hope that the students would have understood "Volume-of 3d shapes". 

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