# VOLUME

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. Formula :

=  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. Formula :

=  (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. Formula :

=  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. Formula :

=  (1/3) x Base area x Height

## 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

=  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

=  48 x 8

Hence the answer is  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 the formula

=  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  =  64 x 8

Hence the answer is 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 the formula

=  (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  =  (1/2) x 28 x 3

Hence the answer is 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 the formula

=  (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 =  (1/2) x 96 x 3

Hence the answer is  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 the formula

=  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 =  12 x 8

Hence the answer is  96 cubic cm

Problem 6 :

Find the volume-of the pyramid given below. Solution :

By using the formula  (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  =  (1/3) x 64 x 9

Hence the answer is 192 cubic cm

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