Question

a cuboid is 10cm long , 6cm broad and 4cm high and a cube has an edge of 7cm . which one has the greatest volume​

Answer 1

Given :-

• Dimensions of cuboid
• length (l) 10cm
• breadth (b) =6cm and height (h)= 4cm

• Dimension of cube =7cm

To find :-

We have to find that which one have greater volume

A.T.Q

$\boxed{\sf{Volume\:of\:cuboid=l\times b\times h}}$

$\boxed{\sf{Volume\:of\:cube=side{}^{3}}}$

So first find the volume of cuboid

$\sf\implies Volume \:of\:cuboid=l\times b\times h\\ \\ \sf\implies Volume =10\times 6\times 4\\ \\ \sf\implies Volume =60\times 4\\ \\ \sf\implies Volume\:of\:cuboid=240cm{}^{3}$

Now find the volume of cube

$\sf\implies Volume\:of\:cube=side{}^{3}\\ \\ \sf\implies Volume\:of\:cube=(7){}^{3}\\ \\ \sf\implies Volume =7\times 7\times 7\\ \\ \sf\implies Volume \:of\:cube=343cm{}^{3}$

$\sf \:\:Volume\:of\:cuboid=\boxed{\sf{240cm{}^{3}}}$

$\sf\:\:\:Volume\:of\:cube=\boxed{\sf{343cm{}^{3}}}$

So cube has greater volume !!

Answer 2

Answer: Given cube has greater volume than cuboid

Step-by-step explanation

Given data :

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   CUBOID DIMENSIONS

length:  10 cm

breadth:6 cm

height :  4 cm

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CUBE DIMENSIONS

length of the edge of the  cube  : 7 cm

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QUESTION :

To identify whether cube or cuboid has greater volume.

so , lets find out their volumes respectively

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CUBOID VOLUME :

l × b × h

10 × 6 × 4

240 cm^3.

CUBE VOLUME :

$s^{3}$

$7^{3}$

343 cm^3

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therefore by calculations ,  given Cube has greater volume than cuboid .

HOPE IT HELPS !!!