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Cubes and Cube Roots

Short Answer Type

11.

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

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Long Answer Type

12.

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. (i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704

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Short Answer Type

13. 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?

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14.

Find the cube root of 1728.

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15.

Fint the cube root of 27000 by prime factorisation.

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

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17. What is the smallest number by which 288 must be multiplied so that the product is a perfect cube?

Resolving 288 in to prime factors, we have

i.e. 288 = 2 x 2 x 2 x 2 x 2 x 3 x 3
Grouping the factors in triple, we get
288 = [2 x 2 x 2] x 2 x 2 x 3 x 3

We observe that if 288 is multiplied by (2 x 3), then its prime factors will exist in triples.

Thus, the required smallest number by which 288 be multiplied to make it a perfect cube i: (2 x 3), i.e. 6.

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18.

Fint the cube of $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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19. Show that 0.001728 is the cube of a rational number. Find that rational number whose cube is 0.0017288.

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20. The volume of a cubical box is 64 cm³. What is its side?

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