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**

**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".

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