VOLUME OF PRISM WORKSHEET

Problem 1 :

Find the volume of the cuboid shown below.

Problem 2 :

Find the volume of the cube shown below. 

Problem 3 :

Find the volume of the triangular prism given below.

Problem 4 :

Find the volume of the triangular prism shown below.

Problem 5 :

Find the volume of the triangular prism shown below. 

Problem 6 :

Find the volume of the pyramid shown below.

Problem 7 :

Shown below is a prism. The cross-sectional area is 21 cm². The prism has a length of 6 cm.

Find the volume of the prism.

Problem 8 :

Describe and correct the error in finding the volume of the triangular prism.

Problem 9 :

As a gift, you fill the calendar with packets of chocolate candy. Each packet has a volume of 2 cubic inches. Find the maximum number of packets you can fi t inside the calendar.

Problem 10 :

Two liters of water are poured into an empty vase shaped like an octagonal prism. The base area is 100 square centimeters. What is the height of the water? (1 L = 1000 cm³)

1. Answer :

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

Then, formula for volume of the above cuboid is

= Base Area x Height

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

Area of base is

= 12 x 4 = 48 cm²

Height of the cuboid is 8 cm.

So, volume of the above cuboid is

= 48 x 8

= 384 cm³

2. Answer :

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

Then, formula for volume of the above cube is

= Base area x Height

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

Area of base is

= 8 x 8

= 64 cm²

Height of the cube is 8 cm.

So, volume of the above cube is

= 64 x 8

= 512 cm³

3. Answer :

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

Then, formula for the above triangular prism is

= (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 is

= 7 x 4

= 28  cm²

Height of the prism is 3 cm.

So, volume of the above triangular prism is

= (1/2) x 28 x 3

= 42 cm³

4. Answer :

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

Then, formula for the above triangular prism is

= (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 is

= 12 x 8

= 96 cm²

Height of the prism is 3 cm.

So, volume of the above triangular prism is

= (1/2) x 96 x 3

= 144 cm³

5. Answer :

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

Then, formula for the above triangular prism is

= Base area x Height

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

So, area of the base is

= (1/2) x 6 x 4

= 12 cm²

Height of the prism is 8 cm.

So, volume of the above triangular prism is

= 12 x 8

= 96 cm³

6. Answer :

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

Then, formula for the above triangular prism is

= (1/3) x Base area x Height

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

So, area of the base is

= 8 x 8

= 64 cm²

Height of the pyramid is 9 cm.

So, volume of the above triangular prism is

= (1/3) x 64 x 9

= 192 cm³

7. Answer :

Base area of pentagon = 21 cm²

Height = 6 cm

Volume of pentagon shaped prism = base area x height

= 21 x 6

= 126 cm³

8. Answer :

In the given triangular base prism, the base is in the shape of right triangle

Base area = (1/2) x base x height

= (1/2) x 5 x 7

= 35/2

= 17.5 cm²

Height = 10 cm

Volume of the triangular prism = base area x height

= 17.5 x 10

= 175 cm³

9. Answer :

Volume of calender = (1/2) x base x height of triangle x height of prism

= (1/2) x 4 x 6 x 8

= 2 x 6 x 8

= 96 cubic inches

Volume of each packet = 2 cubic inches

Number of packets to be filled = 96/2

= 48 packets.

10. Answer :

1 liter = 1000 cm³

2 liter = 2000 cm³

Capacity of octagonal prism = base area x height

2000 = 100 x h

2000/100 = h

h = 20 cm

So, the required height of the octagonal prism is 20 cm.

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