Solving Math Class 5 Page 128 Textbook, Concentrated Practice, Solve exercises 1, 2, 3

Step-by-step guide to solving Math Class 5 Page 128 (including solution methods)

1. Solve Exercise 1 - Solve Math 5 Page 128 

Problem:
A rectangular glass tank used for fish has dimensions of 1m in length, 50cm in width, and 60cm in height.
a) Calculate the area of the glass used for the fish tank (without a lid).
b) Calculate the volume of the fish tank.
c) The water level in the tank is 3/4 of the tank's height. Calculate the volume of water in the tank (ignoring the thickness of the glass).

Solution Method:
- Convert length units from meters/centimeters to decimeters.
- Solution method:
a) Calculate the surrounding area of the glass tank by adding the surrounding area of the glass tank to the bottom surface area.
b) Calculate the volume of the fish tank by applying the formula for the volume of a rectangular prism: V = length x width x height.
c) To find the volume of water in the tank, multiply the volume of the fish tank by 3/4.

Answer:
Convert 1m = 10dm; 50cm = 5dm; 60cm = 6dm.
a) The surrounding area of the glass tank is:
(10 + 5) x 2 x 6 = 180 (dm²)
The bottom surface area of the glass tank is:
10 x 5 = 50 (dm²)
The area of the glass used is:
180 + 50 = 230 (dm²)
b) The volume of the fish tank is:
10 x 5 x 6 = 300 (dm³)
300 dm³ = 300 liters
c) The volume of water in the tank is:
300 x 3/4 = 225 (liters)
Results:
a) 230 dm²;
b) 300 liters;
c) 225 liters.

2. Solve Exercise 2 - Solve Math Class 5 Concentrated Practice Page 128

Problem:
A cube with a side length of 1.5m. Calculate:
a) Surface area of the cube;
b) Total surface area of the cube;
c) Volume of the cube.

Solution Method:
- Formula for the surface area of the cube: S = a x a x 4 (Surface area of the cube is the square of the side length multiplied by 4).
- Formula for the total surface area of the cube: S = a x a x 6 (Total surface area of the cube is the square of the side length multiplied by 6).
- Formula for the volume of the cube: V = a x a x a (where: V is the volume; a is the side length of the cube).

Answer:
a) Surface area of the cube is:
1.5 x 1.5 x 4 = 9 (m²)
b) Total surface area of the cube is:
1.5 x 1.5 x 6 = 13.5 (m²)
c) Volume of the cube is:
1.5 x 1.5 x 1.5 = 3.375 (m³)
Results:
a) 9m²;
b) 13.5m²;
c) 3.375m³

3. Solve Exercise 3 - Solve Math Class 5 Concentrated Practice Page 128

Problem:
There are two cubes. Cube M has a side length 3 times that of Cube N.
a) How many times is the total surface area of Cube M greater than the total surface area of Cube N?
b) How many times is the volume of Cube M greater than the volume of Cube N?

Solution Method:
- Formula for the total surface area of a cube: S = a x a x 6 (S is the surface area; a is the side length).
- Formula for the volume of a cube: V = a x a x a (S is the surface area; a is the side length).

Answer:
Let the side length of Cube N be a. So, the side length of Cube M is a x 3.
a) The total surface area of Cube N is:
a x a x 6
The total surface area of Cube M is:
(a x 3) x (a x 3) x 6 = (a x a x 6) x (3 x 3) = (a x a x 6) x 9
Therefore, the total surface area of Cube M is 9 times greater than the total surface area of Cube N.
b) The volume of Cube N is:
a x a x a
The volume of Cube M is:
(a x 3) x (a x 3) x (a x 3) = (a x a x a) x (3 x 3 x 3) = (a x a x a) x 27
Therefore, the volume of Cube M is 27 times greater than the volume of Cube N.

Math Class 5 Guide Page 128 (concise)