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Cubes And Cube Roots

Question

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Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

Solution

Sides of the cubiod are 5 cm, 2 cm, 5 cm

∴ Volume of the cubiod = 5 cm x 2 cm x 5 cm
To form is as a cube its dimension should be in the group of triples.

∴ Volume of the required cube = [5 cm x 5 cm x 2 cm] x 5 cm x 2 cm x 2 cm
= [ 5 x 5 x 2 cm³] x 20 cm³
Thus, the required number of cubiods = 20.

Some More Questions From Cubes and Cube Roots Chapter

Check which of the following are perfect cubes.

(i) 2700 (ii) 16000 (iii) 64000 (iv) 900

(v) 125000 (vi) 36000 (vii) 21600 (viii) 10000

(ix) 27000000 (x) 1000

What pattern do you observe in these perfect cubes?

Which of the following numbers are not perfect cubes? (i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656

Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100

Show that —1728 is a perfect cube. Also, find the number whose cube is – 1728.

Is 216 a perfect cube? What is the number whose cube is 216?

Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

Find the cube root of 1728.

Fint the cube root of 27000 by prime factorisation.

State true or false: for any integer m, m² < m³. Why?

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