﻿ Area and Volume Worksheet | Problems & Solutions

# 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.]

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.]

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.

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.

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.

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.

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.

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.

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.

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.