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Area and Volume Worksheet

Area and Volume Worksheet
  • Page 1
 1.  
Find the area of the design made by Michelle.

a.
4 square feet
b.
5 square feet
c.
6 square feet
d.
2 square feet


Solution:

In the given grid, there are 2 cells fully shaded and 4 cells half shaded.
Total shaded cells = 2 + ( 4 × 1 / 2 ) = 4

Area of shaded region = Number of cells in the shaded region × Area of each cell in the grid
[Substitute the values.]

= 4 × 1 = 4 square feet.
[Given area of each shaded cell = 1 square feet.]


Correct answer : (1)
 2.  
If the area of each cell in the grid is 1 square unit, what is the area of the non-shaded region in the figure?


a.
64 square units
b.
4 square units
c.
40 square units
d.
24 square units


Solution:

Area of the non-shaded region = Total number of cells in the grid - Area of shaded region.

Area of the shaded region = Number of cells in the shaded region × Area of each cell in the grid
[There are 40 shaded cells in the grid.]

= 40 × 1
[Substitute the values.]

= 40
[Multiply.]

The area of the shaded region in the figure is 40 square units.

Therefore, Area of non-shaded region = 64 - 40 = 24 square units.
[Total number of cells = 64.]


Correct answer : (4)
 3.  
The area of each cell in the grid is 1 square unit. Find the area of the shaded region.

a.
32 units
b.
32 square units
c.
36 square units
d.
28 square units


Solution:

In the figure, there are 36 shaded cells.

Area of the shaded region = 36 × area of each cell in the grid

= 36 × 1
[Substitute the area of each cell with 1.]

= 36
[Multiply.]

The area of the shaded region in the figure is 36 square units.


Correct answer : (3)
 4.  
The area of each cell on the grid is 1 square unit. Find the area of the shaded rectangle.

a.
15 square units
b.
16 units
c.
12 square units
d.
14 square units


Solution:

In the figure, there are 12 shaded cells.

Area of the shaded rectangle = 12 × area of each cell in the grid

= 12 × 1
[Substitute the area of each cell with 1.]

= 12
[Multiply.]

The area of the shaded rectangle in the figure is 12 square units.


Correct answer : (3)
 5.  
The area of each cell on the grid is 1 square unit. Find the area of the shaded region.

a.
16 square units
b.
10 square units
c.
15 square units
d.
12 units


Solution:

In the figure, there are 10 shaded cells.

Area of the shaded region = 10 × area of each cell in the grid

= 10 × 1
[Substitute the area of each cell with 1.]

= 10
[Multiply.]

The area of the shaded region in the figure is 10 square units.


Correct answer : (2)
 6.  
The area of each cell in the grid is 1 square unit. Find the area of the shaded region.


a.
16 units
b.
10 square units
c.
20 square units
d.
4 square units


Solution:

In the figure, there are 10 shaded cells.

Area of the shaded region = 10 × area of each cell in the grid

= 10 × 1
[Substitute the area of each cell with 1.]

= 10
[Multiply.]

The area of the shaded region in the figure is 10 square units.


Correct answer : (2)
 7.  
Find the area of the shaded region shown, if the area of each cell in the grid is 1 square unit.

a.
10 square units
b.
12 square units
c.
9 square units
d.
7 square units


Solution:

In the figure there are 10 shaded cells.

Area of shaded region = 10 × area of each cell in the grid

= 10 × 1

= 10

The area of the shaded region in the figure is 10 square units.


Correct answer : (1)
 8.  
What could be the volume of the following shape?

a.
4 cubic units
b.
9 cubic units
c.
6 cubic units
d.
8 cubic units


Solution:

Volume of the solid = number of units × volume of each unit.

Volume = 8 × 1 cubic unit = 8 cubic units.


Correct answer : (4)
 9.  
Find the area of the shaded region.


a.
10 square units
b.
11 square units
c.
9 square units
d.
12 square units


Solution:

In the grid 11 squares are shaded.
[Count the number of shaded squares in the grid.]

Since the area of each square is 1 square unit, area of 11 squares = 11 × 1 = 11 square units.

So, the area of the shaded region is 11 square units.


Correct answer : (2)
 10.  
Find the area of the shaded region.


a.
13 square units
b.
12 square units
c.
11 square units
d.
10 square units


Solution:

In the grid 10 squares are shaded.
[Count the number of shaded squares in the grid.]

Since the area of each square is 1 square unit, area of 10 squares = 10 × 1 = 10 square units.

So, the area of the shaded region is 10 square units.


Correct answer : (4)

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