Grade 5 Math Page 121 - Rectangular Prism Volume

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Guidelines for solving Grade 5 Math Page 121 (including solution methods)

1. Solving Exercise 1 - Grade 5 Math Page 121

Exercise:
Calculate the volume of a rectangular box with length a, width b, and height c:

Solution Method:
The formula for calculating the volume of a rectangular box is extremely simple: V = a x b x c (where: V is the abbreviation for volume; a is the length; b is the width; c is the height).
=> The volume of a rectangular box equals the product of its length, width, and height.

Answer:

2. Solving Exercise 2 - Grade 5 Math Rectangular Prism Volume Page 121

Exercise:
Calculate the volume of the wooden block shaped like the figure below:

Solution Method:
- Step 1: Divide the given wooden block into smaller rectangular boxes
- Step 2: Calculate the volume of each small rectangular box using the formula: V = a x b x c

Answer:
Approach 1:
Divide the wooden block into two rectangular boxes A and B as shown below.

Volume of rectangular box A is:
8 x (12 - 6) x 5 = 240 (cm³)
Volume of rectangular box B is:
15 x 6 x 5 = 450 (cm³)
Volume of the wooden block is:
240 + 450 = 690 (cm³)
Approach 2:
Divide the wooden block into two rectangles C and D as shown below:

Volume of rectangular box C is:
12 x 8 x 5 = 480 (cm³)
Volume of rectangular box D is:
(15 - 8) x 6 x 5 = 210 (cm³)
Volume of the wooden block is:
480 + 210 = 690 (cm³)
 

3. Solving Exercise 3 Grade 5 Math Page 121

Exercise:
Calculate the volume of a stone submerged in a water tank.

Method:
For this exercise, students can solve it in 2 ways:
* Method 1:
- Step 1: Calculate the volume of water in the water tank using the formula: Volume of rectangular prism = Length x Width x Height (for a water tank with dimensions 10cm, 10cm, 5cm).
- Step 2: Calculate the volume of water and the stone in the water tank using the formula: Volume of rectangular prism = Length x Width x Height (for a water tank with dimensions 10cm, 10cm, 7cm).
- Step 3: Calculate the volume of the stone by subtracting the volume of water in the tank from the total volume of water and the stone in the tank.
* Method 2: 
- First, calculate the height of the water level by subtracting the height of the water tank with both water and stone from the height of the water tank with only water.
- Next, calculate the volume of the water level by multiplying the length by the width, then further multiplying by the height of the water level obtained.

Answer:
Method 1: 
The volume of water in the tank is:
10 x 10 x 5 = 500 (cm³)
The total volume of water and the stone is:
10 x 10 x 7 = 700 (cm³)
The volume of the stone is:
700 - 500 = 200 (cm³)
Method 2:
The height of the water level is:
7 - 5 = 2 (cm)
The volume of the water level is:
10 x 10 x 2 = 200 (cm³)
=> This is also the volume of the stone.
Answer: 200 cm³
Additional Note: This is the method that the famous Roman scholar Archimedes used to calculate the volume of the very complex crown of the king 23 centuries ago.

Short Guide to Grade 5 Math Page 121

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Here is the solution for Grade 5 Math Page 121, which is part of the Grade 5 math exercise solution section. Students can review the solutions for Grade 5 Math Page 118 previously solved or preview the solutions for Grade 5 Math Pages 122, 123 to improve their understanding of Grade 5 Math.