Grade 8 Cubes and Cube Roots Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(16) if the Length of Each Side of a Cube is Reduced to One Third of Its Original Value, then Express Its New Volume as a Fraction of Its Original Volume

• For the cube root first we identify its prime factor as below,

• Now for cube root:

• Cube root of
• For the cube root first we identify its prime factor as below

• Now,

• For the cube root of

• Prime factor of 512 are,

• Prime factor of 5832 are,

• So,

• For the cube root of,

• Now, prime factor of 592704 are,

• Now, prime factor of 74088 are,

• Now,

• Given equation,

• Now first,

• Now,

• Now,

• Now,

• Given equation,

• Now,

• Now,

• Now,

• Then ,

• Now,

• Then,

• Now,

• Now,

• Now,

• Here given number is 5400.
• Now perfect cube number is a number of multiplication of three identical integer numbers.
• For find out the identical number; list out its prime factor
• So,
• From above its clear that “5” remains without pair of three identical number
• So, smallest number that must multiply to make number 5400 perfect cube is: “5”
• So,
• And, smallest number that must divide to make number 5400 perfect cube is:
• So,

• Here given number is 18522.
• Now perfect cube number is a number of multiplication of three identical integer number.
• For find out the identical number; list out its prime factor
• So,

• From above its clear that “” remains without pair of three identical number
• So, smallest number that must multiply to make number 18522 perfect cube is: “
• So,
• And, smallest number that must divide to make number 18522 perfect cube is:
• So,
• Therefore,

• Here given number is 3316.
• Now perfect cube number is a number of multiplication of three identical integer number.
• For find out the identical number; list out its prime factor
• So,

• From above its clear that “” remains without pair of three identical number
• So, smallest number that must multiply to make number 3136 perfect cube is: “
• So,
• And, smallest number that must divide to make number 3136 perfect cube is:
• So,
• Therefore,

• Here given number is 1372.
• Now perfect cube number is a number of multiplication of three identical integer number.
• For find out the identical number; list out its prime factor
• So,

• From above its clear that “” remains without pair of three identical number
• So, smallest number that must multiply to make number 1372 perfect cube is: “
• So,
• And, smallest number that must divide to make number 1372 perfect cube is:
• So,
• Therefore,

• Here given number is 8232.
• Now perfect cube number is a number of multiplication of three identical integer number.
• For find out the identical number; list out its prime factor
• So,

• From above its clear that “” remains without pair of three identical number
• So, smallest number that must multiply to make number 8232 perfect cube is: “
• So,
• And, smallest number that must divide to make number 8232 perfect cube is:
• So,
• Therefore,

• Here consider cube of last digit (unit digit) only;

• Here 8 itself is a unit digit.
• So,

• Here consider cube of last digit (unit digit) only;

• Here from 729; 9 is at unit place.
• So,

• Here consider cube of last digit (unit digit) only;

• Here from 64; 4 is at unit place.
• So,

• To identify the unit digit of given number cube root, first we should know the cube of the unit digit.
• That means
• Now,

• Here to identify the unit digit of cube root of given number we consider only last digit (unit digit) of given number;
• Now, we know that
• Therefore,

• To identify the unit digit of given number cube root, first we should know the cube of the unit digit.
• That means
• Now,

• Here to identify the unit digit of cube root of given number we consider only last digit (unit digit) of given number;
• Now, we know that

• To identify the unit digit of given number cube root, first we should know the cube of the unit digit.
• That means
• Now,

• Here to identify the unit digit of cube root of given number we consider only last digit (unit digit) of given number;
• Now, we know that

• Volume of the cubical box
• Now we know that, volume of cube
• So,

Volume of the cubical box

• Now, for cube root of 117649 ,

• Now,

• So, length of each side of cubical box is 49 m

• Suppose length of each side of cube
• Now,

Volume of cube

• If its length reduced by one third of its original length
• Than;

• Now

• Therefore,

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