Cube Numbers and Solid Figures

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What is the definition of a perfect cube?

A number that has a cube root of 3

A number that can be obtained by multiplying a number by taking it three times (correct)

A number that can only be divided by 3

A number that can be obtained by multiplying a number by 3

Which of the following is a perfect cube?

64

27 (correct)

36

49

Why is 9 not considered a perfect cube?

There is no natural number that multiplied by three times gives 9 (correct)

It is an odd number

It does not have a cube root

It cannot be divided by 3

How many perfect cubes are there from 1 to 1000?

10 (A) Signup and view all the answers

Are the cubes of even numbers always even?

Yes, always (C) Signup and view all the answers

What can you say about the cubes of odd numbers?

They are always odd (B) Signup and view all the answers

Which of the following numbers is not a perfect cube?

128 (C) Signup and view all the answers

What is the smallest number needed to multiply 256 by to obtain a perfect cube?

4 (D) Signup and view all the answers

Which number must each of the following be divided by to obtain a perfect cube: 135?

3 (C) Signup and view all the answers

If Parikshit wants to form a cube with plasticine cuboids of sides 5 cm, 2 cm, 5 cm, how many cuboids will he need?

20 (A) Signup and view all the answers

If the volume of a cube is 125 cm³, what is the length of its side?

$5$ cm (C) Signup and view all the answers

What is the cube root of 8?

$2$ (A) Signup and view all the answers

Which statement about cube numbers is true?

They are obtained by multiplying a number by itself twice. (A) Signup and view all the answers

If the square of a number ends with 5, what can we conclude about its cube?

Its cube will end with 25. (D) Signup and view all the answers

What is a Hardy-Ramanujan Number?

A number that can be expressed as the sum of two cubes in two different ways. (A) Signup and view all the answers

Can the cube of a single-digit number be another single-digit number?

Yes, it can be a single-digit number. (D) Signup and view all the answers

Which type of numbers may have seven or more digits when cubed?

Two-digit numbers. (C) Signup and view all the answers

What is the significance of the number 1729 according to Ramanujan?

It is the smallest number that can be expressed as a sum of two cubes in two different ways. (B) Signup and view all the answers

Why is 1729 known as the Hardy-Ramanujan Number?

Because it is the smallest number that can be expressed as a sum of two cubes in two different ways. (D) Signup and view all the answers

What was Ramanujan known for throughout his life?

For his experiments with numbers and love for mathematical patterns. (D) Signup and view all the answers

In geometry, what characteristic defines a cube?

Having all sides equal in length. (C) Signup and view all the answers

How many cubes of side 1 cm are needed to make a cube of side 2 cm?

4 cubes (B) Signup and view all the answers

How many cubes of side 1 cm are needed to make a cube of side 3 cm?

16 cubes (D) Signup and view all the answers

Which number should 53240 be divided by to make it a perfect cube?

5 (D) Signup and view all the answers

Is 1188 a perfect cube?

No (D) Signup and view all the answers

What is the smallest number that should multiply 68600 to make it a perfect cube?

5 (C) Signup and view all the answers

Which prime factorization indicates a number that is not a perfect cube?

$2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5$ (B) Signup and view all the answers

If a number has prime factors $3^2$, $5$, and $7^3$, is it a perfect cube?

No (B) Signup and view all the answers

What is the result when $2^4 \times 3^3 \times 5^2$ is divided by $2^2 \times 3 \times 5$?

$5^2$ (B) Signup and view all the answers