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Cubes And Cube Roots Test - 2

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Cubes And Cube Roots Test - 2
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  • Question 1
    1 / -0

    The length of each side of a cube is 4.6 cm. Its volume is

    Solution

    Side of the cube = 4.6 cm
    Volume = (side)3
    4.6 × 4.6 × 4.6 = 97.336 cm3

     

  • Question 2
    1 / -0

    What is the smallest number by which 3087 must be divided so that the quotient obtained is a perfect cube?

    Solution

    3087 = 7 × 7 × 7 × 9
    To obtain a perfect cube, we need to divide 3087 by 9.
    So, the correct answer is 9.

     

  • Question 3
    1 / -0

    Akul gave a Mathematical problem to Yamini;

    The difference of two perfect cubes is 387. If the cube root of the greater of the two numbers is 8, find the cube root of the smaller number.

    Help Yamini to find the answer.

    Solution

    The cube root greater number is 8. So, the greater number will be 512.
    Now, the difference is 387. Therefore, the second perfect cube is 512 - 387 = 125.
    Thus, cube root of smaller number is 5.

     

  • Question 4
    1 / -0

    A blacksmith has to make 13 smaller cubes each of side 6 cm after melting the larger cuboidal box of dimensions 12 cm × 13 cm × 21 cm. What will be the volume of the left over material after making new cubes?

    Solution

    Volume of the cuboid = 12 × 13 × 21 = 3276 cm3
    Volume of 1 smaller cube = 6 × 6 × 6 = 216 cm3

    Volume required for 13 smaller cubes = 13 × 216 = 2808 cm3
    Volume of the left over material = 3276 - 2808 = 468 cm3

     

  • Question 5
    1 / -0

    If the side of a cube is 7 cm, what is its volume in mm3?

    Solution

    Volume of the cube = (side)3
    = (7 cm)3 = 343 cm3

    Now, as 1 cm = 10 mm
    343 cm3 = 3,43,000 mm3

    So, the volume of cube is 3,43,000 mm3 .

     

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