Cubes and Cube Roots quiz

Which of the following is a perfect cube?

The cube root of 512 is:

The Hardy-Ramanujan number is:

The units digit of 17^3 is:

The smallest number by which 72 must be multiplied to get a perfect cube is:

The cube of -4 is:

The cube root of 0.027 is:

The number of zeros at the end of the cube of 100 is:

The sum 7 + 9 + 11 is the cube of:

The cube of an odd natural number is always:

Find the cubes of 1.5 and 3/5. (2 marks)

Show by prime factorisation that 1188 is not a perfect cube. (2 marks)

Find the cube root of -1331 using prime factorisation. (2 marks)

Find the smallest number by which 1323 must be multiplied to make it a perfect cube. Write the cube root of the product. (2 marks)

Find the cube roots of 27/64 and 0.001. (2 marks)

Verify that 9^3 + 10^3 = 1^3 + 12^3. (2 marks)

Without finding the cubes, write the units digits of 3331^3, 1005^3, 1024^3 and 77^3. (2 marks)

Find the smallest number by which 81 must be divided so that the quotient is a perfect cube. (2 marks)

Explain why the cube of an even number is always even. Give two examples. (2 marks)

Is 500 a perfect cube? Give a reason using prime factorisation. (2 marks)

Find the cube root of 74088 by prime factorisation. (3 marks)

Using the method of grouping digits, estimate the cube roots of the perfect cubes 175616 and 110592. (3 marks)

Find the smallest number by which 3087 must be divided so that the quotient is a perfect cube. Find the cube root of the quotient. (3 marks)

A cubical water tank has a volume of 42.875 m^3. Find the length of its edge and its capacity in litres (1 m^3 = 1000 L). (3 marks)

Find the cube roots of (i) 2.744 (ii) 0.000216 (iii) -2197/2744. (3 marks)

Read the passage and answer the questions. A toy company makes small wooden cubes of edge 2 cm. It packs them without gaps in cubical boxes of edge 10 cm. (i) Find the volume of one small cube. (ii) How many small cubes fit into one box? (iii) If the edge of the box is doubled to 20 cm, how many small cubes will fit now? (5 marks)

Read the passage and answer the questions. The mathematician G. H. Hardy visited Srinivasa Ramanujan in hospital in a taxi numbered 1729. Hardy said the number seemed dull, but Ramanujan replied that it is the smallest number that can be written as the sum of two cubes in two different ways. (i) Write 1729 as the sum of two cubes in two ways. (ii) Verify that 4104 = 2^3 + 16^3 = 9^3 + 15^3. (iii) Why are such numbers sometimes called taxicab numbers? (5 marks)

Read the passage and answer the questions. Kavya has 2000 identical unit cubes. She wants to build the largest possible solid cube using them. (i) What is the edge of the largest cube she can build? (ii) How many unit cubes will be left over? (iii) How many more unit cubes would she need to build a cube one unit larger in edge? (5 marks)

Read the passage and answer the questions. Amit wrote the number 5400 on the board and asked his friends to change it into a perfect cube in two different ways. (i) Write the prime factorisation of 5400. (ii) Find the smallest number by which it must be multiplied to make a perfect cube, and the cube root of the product. (iii) Find the smallest number by which it must be divided to make a perfect cube, and the cube root of the quotient. (5 marks)

Read the passage and answer the questions. A school builds a cubical water tank of edge 1.2 m on its roof. Later it plans a bigger cubical tank that can hold 8 times as much water. (i) Find the volume of the present tank in m^3. (ii) Find its capacity in litres. (iii) Find the edge of the bigger tank. (5 marks)

Explain the method of finding the cube root of a number by prime factorisation, drawing a factor tree. Use it to find the cube root of 91125. Also show, with a factor tree, why 100 is not a perfect cube. (6 marks)

Explain, step by step, the method of estimating the cube root of a perfect cube by grouping its digits in threes from the right. Use it to find the cube roots of 857375 and 389017, and check one answer by multiplication. (6 marks)

Draw unit-cube models of 1^3, 2^3 and 3^3. Explain the pattern 1 = 1^3, 3 + 5 = 2^3, 7 + 9 + 11 = 3^3, and use it to find the six consecutive odd numbers whose sum is 6^3. (6 marks)

Show that the cube root of a product equals the product of the cube roots, using 27 x 64 as an example. Use this property to find the cube roots of 1728 and 125/343. Explain why the cube of a negative number is negative, with one example. (6 marks)

Draw a factor tree for 6750. Using it, find (i) the smallest number by which 6750 must be multiplied to get a perfect cube, and the cube root of the product (ii) the smallest number by which 6750 must be divided to get a perfect cube, and the cube root of the quotient. (6 marks)