Class 8 Exam > Class 8 Notes > Mathematics Class 8- New NCERT (Ganita Prakash) > Unit Test: A Square And A Cube
Unit Test: A Square And A Cube | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download
Time: 1 hour
M.M. 30
Attempt all questions.
- Question numbers 1 to 5 carry 1 mark each.
- Question numbers 6 to 8 carry 2 marks each.
- Question numbers 9 to 11 carry 3 marks each.
- Question numbers 12 & 13 carry 5 marks each
Q1: Which of the following is NOT a possible units digit of a perfect square? (1 Mark)
a) 1
b) 4
c) 7
d) 9
Q2: How many perfect squares are there between 1 and 100 (inclusive)? (1 Mark)
a) 9
b) 10
c) 11
d) 12
Q3: Which of the following numbers is the smallest Taxicab Number? (1 Mark)
a) 4104
b) 13832
c) 1729
d) 1000
Q4: In prime factorisation, a number is a perfect square if: (1 Mark)
a) All prime factors occur in odd powers
b) All prime factors occur in even powers
c) It has more than 2 prime factors
d) It is greater than 100
Q5: The cube of 10 can be expressed as the sum of: (1 Mark)
a) 10 consecutive odd numbers
b) 10 consecutive even numbers
c) 20 consecutive odd numbers
d) 5 consecutive odd numbers
Q6: A square park has an area of 6400 m². Find the length of one side. (2 Marks)
Q7: If x² = 2116, find x. (2 Marks)
Q8: A cube has a volume of 2197 cm³. Find the length of one edge. (2 Marks)
Q9: Find the least number that must be subtracted from 1200 to make it a perfect square. Also, find that perfect square. (3 Marks)
Q10: Find the least number by which 1323 must be divided so that the quotient is a perfect cube. Also, find the cube root of the quotient. (3 Marks)
Q11: A square garden has an area of 3136 m². If the length and width are equal, find the length of one side of the garden. (3 Marks)
Q12: The Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, find the cube root of the larger number. (5 Marks)
Q13: Find the number of plants in each row if 1024 plants are arranged so that the number of plants in a row is the same as the number of rows. (5 Marks)
You can access the solutions to this Unit Test here.
The document Unit Test: A Square And A Cube | Mathematics Class 8- New NCERT (Ganita Prakash) is a part of the Class 8 Course Mathematics Class 8- New NCERT (Ganita Prakash).
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FAQs on Unit Test: A Square And A Cube - Mathematics Class 8- New NCERT (Ganita Prakash)
| 1. What are the key differences between a square and a cube in geometry? |  |
Ans. A square is a two-dimensional shape with four equal sides and four right angles, while a cube is a three-dimensional shape with six equal square faces. In a square, only the length and width are measured, whereas a cube has length, width, and height.
| 2. How can we calculate the area of a square and the surface area of a cube? | |
Ans. The area of a square is calculated using the formula A = side², where "side" is the length of one side of the square. The surface area of a cube is calculated with the formula SA = 6 × side², as each of the six faces is a square with the same area.
| 3. What are some real-life examples of squares and cubes? | |
Ans. Real-life examples of squares include tiles, books, and windows, which often have a square shape. Cubes can be seen in dice, boxes, and ice cubes. These shapes are commonly found in everyday objects.
| 4. How do squares and cubes relate to the concepts of perimeter and volume? | |
Ans. The perimeter of a square is calculated using the formula P = 4 × side, while a cube's volume is determined using the formula V = side³. The perimeter gives the distance around the square, whereas the volume measures the space occupied by the cube.
| 5. Can you explain the significance of squares and cubes in mathematical concepts like the Pythagorean theorem? | |
Ans. Squares are fundamental in the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²). Cubes, while not directly involved in this theorem, are important in higher mathematics and in understanding three-dimensional space.
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