Important Questions on A Square and A Cube for Class 8

Important Questions on A Square and A Cube for Class 8 are available in this Maths article. Important Questions on A Square and A Cube for Class 8 are very useful to solve the problems easily. This article helps the students to know the key questions and answers about A Square and A Cube. A square shows the result of multiplying a number by itself once, and a cube shows the result of multiplying a number by itself twice. Our subject experts have solved these problems step by step as per the CBSE syllabus and NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination.

Table of Contents

• Square Formulas
• Cube Formulas
• Exercise 1: Basic Concept Questions
• Exercise 2: Area and Perimeter of Squares
• Exercise 3: Volume and Surface Area of Cubes
• Exercise 4: Word Problems on Squares
• Exercise 5: Word Problems on Cubes
• Exercise 6: Mixed Problems (Squares and Cubes)
• Exercise 7: Challenging Questions
• Tips for Understanding A Square and A Cube
• Most Common Examination Questions (Board Exams)

Square Formulas

• Area of Square = side × side = a²
• Perimeter of Square = 4 × side = 4a
• Diagonal of Square = a√2 (where a is the side length)

Cube Formulas

• Volume of Cube = side × side × side = a³
• Total Surface Area of Cube = 6a²
• Lateral Surface Area of Cube = 4a²
• Space Diagonal of Cube = a√3 (where a is the side length)

Exercise 1: Basic Concept Questions

Question 1: What is a square?

Solution: A square is a two-dimensional shape with:

• 4 equal sides
• 4 right angles

Question 2: What is the perimeter of a square?

Solution: The perimeter is the total length of all sides.

P=4a

where a is the side length.

Question 3: What is the area of a square?

Solution: The area is the space covered inside the square.

A=a2

Question 4: What is a cube?

Solution: A cube is a three-dimensional solid having:

• 6 square faces
• 12 edges
• 8 vertices

Question 5: What is the volume of a cube?

Solution:

The formula for the volume of a cube is: V=a3

where:

•   V = Volume
•   a = Length of one side (edge) of the cube

Exercise 2: Area and Perimeter of Squares

Question 5: Find the area of a square with side 8 cm.

Answer: Area of square = side × side = 8 × 8 = 64 cm²

Question 6: The area of a square is 81 square meters. Find the length of its side.

Answer: Area = side² = 81, so side = √81 = 9 meters

Question 7: Find the perimeter of a square with side 5 cm.

Answer: Perimeter = 4 × side = 4 × 5 = 20 cm

Question 8: The perimeter of a square is 40 inches. Find its area.

Answer: Perimeter = 4 × side = 40, so side = 40 ÷ 4 = 10 inches. Area = side² = 10² = 100 square inches

Question 9: Find the diagonal of a square with side 6 cm.

Answer: Diagonal = side × √2 = 6 × √2 = 6√2 ≈ 8.49 cm

Exercise 3: Volume and Surface Area of Cubes

Question 10: Find the volume of a cube with side 4 cm.

Answer: Volume = side³ = 4³ = 4 × 4 × 4 = 64 cm³

Question 11: The volume of a cube is 125 cubic meters. Find the length of its side.

Answer: Volume = side³ = 125, so side = ∛125 = 5 meters

Question 12: Find the total surface area of a cube with side 3 cm.

Answer: Total surface area = 6 × side² = 6 × 3² = 6 × 9 = 54 cm²

Question 13: Find the lateral surface area of a cube with side 5 cm.

Answer: Lateral surface area = 4 × side² = 4 × 5² = 4 × 25 = 100 cm²

Question 14: The total surface area of a cube is 216 square cm. Find its volume.

Answer: Total surface area = 6a² = 216, so a² = 36, which means a = 6 cm. Volume = 6³ = 216 cm³

Exercise 4: Word Problems on Squares

Question 15: A square garden has a side of 12 meters. What is its area?

Answer: Area = side² = 12² = 144 square meters

Question 16: A square room has an area of 49 square feet. How much fencing is needed to enclose it?

Answer: Area = 49 sq ft, so side = 7 feet. Fencing needed (perimeter) = 4 × 7 = 28 feet

Question 17: A square cloth has a side of 2.5 meters. Find its area in square centimeters.

Answer: Side = 2.5 m = 250 cm. Area = 250² = 62,500 cm²

Question 18: The area of a square tile is 100 cm². If tiles are arranged to form a larger square with 5 tiles on each side, what is the area of the larger square?

Answer: Area of one tile = 100 cm².

Total tiles = 5 × 5 = 25 tiles.

Total area = 25 × 100 = 2,500 cm²

Exercise 5: Word Problems on Cubes

Question 19: A cubic container has a side of 10 cm. How much water can it hold?

Answer: Volume = side³ = 10³ = 1,000 cm³ = 1 liter

Question 20: A cubic box has a surface area of 150 square meters. Find the volume of the box.

Answer: Surface area = 6a² = 150, so a² = 25, which means a = 5 meters. Volume = 5³ = 125 cubic meters

Question 21: How many smaller cubes with side 2 cm can be cut from a larger cube with side 8 cm?

Answer: Volume of larger cube = 8³ = 512 cm³. Volume of smaller cube = 2³ = 8 cm³. Number of smaller cubes = 512 ÷ 8 = 64 cubes

Question 22: A cubic storage box has a side of 6 meters. Find its total surface area and volume.

Answer: Total surface area = 6 × 6² = 6 × 36 = 216 m². Volume = 6³ = 216 m³

Exercise 6: Mixed Problems (Squares and Cubes)

Question 23: Which is greater: the area of a square with side 8 cm or the total surface area of a cube with side 4 cm? By how much?

Answer: Area of square = 8² = 64 cm².

Surface area of cube = 6 × 4² = 96 cm².

Difference = 96 - 64 = 32 cm².

The cube's surface area is greater by 32 cm².

Question 24: A square has the same numerical value for its area as a cube has for its volume. The side of the square is 3 units. What is the side of the cube?

Answer: Area of square = 3² = 9 square units.

If cube volume = 9.

then side³ = 9.

so side = ∛9 ≈ 2.08 units

Question 25: Is 64 a perfect square, a perfect cube, or both? Explain.

Answer: 64 is both a perfect square and a perfect cube. 64 = 8² (perfect square) and 64 = 4³ (perfect cube).

Exercise 7: Challenging Questions

Question 26: Find the side of a cube whose surface area is equal to the area of a square with side 12 cm.

Answer: Area of square = 12² = 144 cm².

Surface area of cube = 6a² = 144,

so a² = 24, which means a = √24 = 2√6 ≈ 4.90 cm

Question 27: Two cubes have sides in the ratio 1:2. What is the ratio of their volumes?

Answer: Let sides be a and 2a.

Volumes are a³ and (2a)³ = 8a³.

Ratio = a³ : 8a³ = 1 : 8

Question 28: If the side of a square is increased by 50%, by what percentage does its area increase?

Answer: Original side = a, area = a².

New side = 1.5a, area = (1.5a)² = 2.25a².

Increase = 2.25a² - a² = 1.25a².

Percentage increase = (1.25a² / a²) × 100 = 125%

Question 29: A cube is painted on all sides and then cut into 27 smaller cubes of equal size. How many cubes will have all three faces painted?

Answer: When a cube is cut into 27 smaller cubes (3×3×3), the cubes with all three faces painted are at the corners only. There are 8 corner cubes, so the answer is 8.

Question 30: If the volume of a cube is 1,000 cm³, find the length of its space diagonal.

Answer: Volume = a³ = 1,000, so a = 10 cm. Space diagonal = a√3 = 10√3 ≈ 17.32 cm

Tips for Understanding A Square and A Cube

1. Learn Perfect Squares First
2. Memorize Perfect Cubes
3. Understand the Difference Between Square and Cube
4. Use Visual Learning Methods
5. Practice Real-World Applications
6. Check Your Answers
7. Learn the Formulas Properly
8. Practice Different Types of Problems

Most Common Examination Questions (Board Exams)

12 Mark Questions (Very Frequently Asked)

1. Find the square of 24.

2. Find the cube of 9.

3. What is the square root of 144?

4. Find the cube root of 216.

5. Is 625 a perfect square?

6. Is 343 a perfect cube?

7. Write the square of 15.

8. Write the cube of 12.

9. Find the smallest square number divisible by 8.

10. What is the cube root of 729?

3 - 4 Mark Questions (Frequently Asked)

1. Find the square root of 2025 using prime factorisation.

2. Find the cube root of 3375 using prime factorisation.

3. Find the least number that must be multiplied by 98 to make it a perfect square.

4. Find the smallest number by which 432 should be divided to get a perfect cube.

5. A square garden has side length 18 m. Find its area.

6. Find the cube of 23 using identity methods.

7. Determine whether 1764 is a perfect square. Give reasons.

8. Find the smallest perfect square divisible by 12, 15, and 20.

9. Simplify √2025.

10. Find the cube root of 2744.

5 - 6 Mark Questions (Less Frequent but Important)

1. Using prime factorisation, find the square root of 9604 and explain each step.

2. A cube-shaped water tank has side length 14 m. Find its volume.

3. Find the smallest perfect cube divisible by 24, 36, and 54.

4. A square playground has area 1600 m². Find the length of each side and perimeter.

5. Find the least number that should be multiplied by 675 to make it a perfect cube.

6. Explain the difference between perfect squares and perfect cubes with examples.

7. Find the cube root of 91125 using prime factorisation.

8. The volume of a cube is 2197 cm³. Find the length of each edge.

9. Find the square root of 5929 by long division method.

10. Solve: If the side of a cube is doubled, how many times does its volume increase?