**Answer: 3.24**

**Question 8**

Write the cubes of all natural numbers between 1 and 20 and verify the following statements

a) Cubes of all odd natural numbers are odd.

b) Cubes of all even natural numbers are even.

**Question 9**

Write cubes of 5 natural numbers which are multiples of 3 and verify the cube of natural number, which is multiple of 3 is multiple of 27.

**Solution Hint**

**Let first 5 multiples of 5 are: 3, 6, 9, 12, 15**

**3**^{3}** = 27 = 27 x 1**

**In all these cases we see that the cube of 3, 6, 9, 12, 15 is also the multiple of 27**

**Hence prove the required result.**

**Question 10**

Which of the following are perfect cube

i)1728 ii) 106480.

**Answer: (i) 1728 is a perfect cube**

**(ii) 106480 is not a perfect cube**

**Question 11**

Which is the smallest number by which 392 must be multiplied so that the product is a perfect cube?

**Answer: 7**

**Question 12**

What is the smallest number by which 8640 must be divided so that the quotient is a perfect cube?

**Answer: 5**

**Question 13**

If one side of a cube is 13 metres, find its volume.

**Answer: 13 x 13 x 13 = 2197**

**Question 14**

Find the cube roots i) 343 ii) 1000

** iii) 2744 iv) 74088 **

**Answer: (i) 7 (ii) 10 (iii) 14 (iii) 42**

**Question 15**

Multiply 137592 by the smallest number so the product is a perfect cube and also find the cube root of product.

**Answer**

**Prime factors of 137592 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 13**

**So if we multiply this number by 7 x 13 x 13 = 1183 then it becomes a perfect cube**

**137592 x 1183 = ****162771336 is a perfect cube**

**Question 16**

The volume of a cube is 343 cubic metres, find one side of cube.

**Answer: 7m**

**Question 17**

Divide the number 26244 by the smallest number so that quotient is a perfect cube. Also find the cube root of the quotient

**Solution Hint:**

**Prime factors of 26244 = 2 x 2 x 3 x 3 x **__3 x 3 x____3__ x __3 x____3 x 3__

**If we divide this number by ****2 x 2 x 3 x 3 = 36, then it becomes a perfect cube**

**26244 ÷ 36 = 729**

**Question 18**

The volume of cube 512 cubic metre. Find the length of the side of the cube.

**Answer: 8m**

**Question 19**

Find the cube roots of each of the following numbers

**i) 8 X 64 ii) - 216 X 1728 iii) 27 X (- 2744) **

**iv) -125 X -3 375 v) - 456533 vi) - 5832000**

**Answer: (i) 8 (ii) -72 (iii) - 3 x 14 = 42 (iv) 75 (v) -77 (vi) -180**

**Question 20**

Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 972. Find the numbers.

**Solution Hint**

**Let numbers are: x, 2x, 3x**

**(x)**^{3} + (2x)^{3} + (3x)^{3} = 972

** x**^{3} + 8x^{3} + 27x^{3} = 972

** 36 x**^{3} = 972

** x**^{3} = 972 / 36

** x**^{3} = 27 ⇒ **x = 3**

**Question 21**

Difference in two perfect cubes is 189. If the cube root of smaller number is 3. Find the cube roots of the larger number.

**Answer: Larger number = 6**

**Solution Hint**

**Let two numbers are a and b**

**a**^{3} – b^{3} = 189 and b
= 3

**a**^{3} – (3)^{3} = 189

**a**^{3} – 27 = 189

**a**^{3} = 189 + 27

**a**^{3} = 216 ⇒ **a = 6**

**Question 22**

Evaluate: **Answer: 8**

**Question 23**

Evaluate: **Answer: 3/16**

**Question 24**

**If **** , then find the value of x.****Ans: 0.03**

**Question 25**

**Find the smallest number by which 2880 must be divided so that the quotient is a perfect cube.**

**Ans. 45**

**THANKS FOR YOUR VISIT**

**PLEASE COMMENT BELOW**

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