Cubes Relation with Cube Numbers

Q.

Write the cubes of all natural numbers between 1 and 10 and verify the following statements:
(i) Cubes of all odd natural numbers are odd
(ii) Cubes of all even natual numbers are even.

Q.

If one side of a cube is $13m$, its volume will be _______.

1. $2744m^3$
2. $2197m^3$
3. $1728m^3$
4. $3375m^3$

Q.

How many cubes of side length 3 can fit in a cuboid of dimension 3×6×9?

1. 2

2. 9

3. 10

4. 6

Q.

If one side of a cube is 13 meters then its volume is ________.

1. $2192m^3$

2. $2197m^3$

3. $2198m^3$

4. $169m^2$

Q.

The volume of a closed cubical tank is 1331 cubic metres. Find the cost of painting its complete surface area from outside at the rate of ₹ 10 per square meter.

1. 7260

2. 7240

3. 7000

4. 7280

Q. Shishir is making a cube of side 6 cm using cubes of sides 2 cm. How many such cubes are needed?

1. 216
2. 27
3. 9
4. 36

Q. value of a cuboid box is 2744000 meter cube. find the length of each side of the box.

Q.

From the given choices select the odd one out:

Q. Calculate the area of a face of a cube if its volume is 216 $c{m}^3$.

1. $36c{m}^2$
2. $72c{m}^2$
3. $144c{m}^2$
4. $288c{m}^2$

Q. If the side of a cube is $x$, then its volume is ___.

1. $x$
2. $x^2$
3. $x^3$
4. $\sqrt[3]{3x}$

Q.

Write the cubes of 5 natural numbers which are of hte form 3n +1(e.g. 4, 7, 10, ...) and erify the following :
'The cube of a natural number of the form 3n + 1 is a natural number of the same form i.e. when divided by 3 it leave the remainder 1 '.

Q.

Write the cubes of 5 natural numbers of the form 3n + 2 (i.e. 5 , 8 , 11, ..... ) and verify the ffollowing
'The cube of a natural number of the form 3n + 2 is a natural number of the same form i.e. when it is divideend by 3 the remainder is 2.

Q.

How many cubes will you remove from $3\times 3\times 3$ rubik's cube of side length 3cm to make it a $2\times 2\times 2$ cube. [3 MARKS]

Q. Shishir is making a cube of side 6 cm using cubes of sides 2 cm. How many such cubes are needed?

1. 9
2. 36
3. 27
4. 216

Q. $\sqrt[3]{3729}+(3{)}^3$ = ________

1. $6^3$
2. $2^5$
3. $6^2$
4. $2^6$

Q.

Question 4 (ii)

A verandah of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find:
The cost of cementing the floor of the verandah at the rate of ₹200 per $m^2$.

Q.

The capacity of a cuboidal tank is $50000litres$ of water. Find the breadth of the tank, if its length and depth are respectively $2.5m$ and $10m.$

Q.

$m^3$ $\ge$ $m^2$ . To satisfy this condition, $m$ can be

1. a positive integer

2. any number between 0 and 1
3. a negative integer
4. 4

Q.

Write cubes of first three multiples of $3$.

Q. If a number is multiplied by 5, then the cube of the new number will become _____ times the cube of the original number.

1. 1
2. 9
3. 64
4. 125

Q.

The cube of average of 3 and 7 will also be the average of the of the cubes of 3 and 7.

1. True

2. False

Q.

Which of the following is a perfect cube?

1. 532

2. 729

3. 827

4. 943

Q. Tick (✓) the correct answer:
How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
(a) 10
(b) 100
(c) 1000
(d) 10000

Q. Match the volume of following solids

1. $a^3$
2. $lbh$
3. $\pi r^{2}h$

Q. The volume of a cubical box is $474.552$ cubic meters. Find the length of each side of the box.​

Q.

The volume of a closed cubical tank is 1331 cubic metre. Find the length of the side of the cubical tank

1. 12 m

2. 13 m

3. 11 m

4. 20 m

Q.

$a^3$ - $b^3$ is always divisible by:

1. a - b

2. a × b

3. a + b

4. 2a + b

Q.

The cube of number obtained by taking the average of 3 and 7 will be equal to the avearge of cubes of 3 and 7.

1. True

2. False

Q.

The cube of a number is less than its square in which of the following cases ?

1. The number lies between -1 and 0

2. The number is 0

3. The number lies between 0 and 1
4. The number lies between 1 and 2

Q.

Question 115

Solve the following question:

If one side of a cube is 15 m in length, then find its volume.