Question

A cuboid is 7 cm long, 5 cm broad and 8 cm high and a cube has an edge of 8
cm Which one has a greater volume?

Answer 1

AnswEr-:

• $\underline{\boxed {\mathrm {\dag{\red{Volume\:of\:Cube\:is\: greater\:than\:Volume\:of\:Cuboid }}}}}$

Explanation-:

• $\mathrm { Given-:}$

In Cuboid-:

• Length of Cuboid-: 7 cm
• Breadth of Cuboid-: 5cm
• Height of Cuboid-: 8cm

In Cube -:

• Edge of Cube-: 8 cm

• $\mathrm { To\:Find-:}$

• Which one has greater volume cube or Cuboid .

$\dag{\mathrm {Solution \:of\:Question-:}}$

• $\underbrace {\mathrm { Understanding \:The\:Concept-:\:}}$

• Which one of the shape has greater volume.

• For this we have to find the volume of Each shape by putting known and Given Values in the Formula of that shapes .

• By this we can get the which shape has greater Volume.

Volume of Cuboid-:

As , We know that ,

• $\underline {\boxed{\dag{\red{\mathrm{ Volume_{(\:Cuboid)} = Length\times Breadth \times Height\:cubic.m}}}}}$

Here ,

• Length of Cuboid-: 7 cm
• Breadth of Cuboid-: 5cm
• Height of Cuboid-: 8cm

Now , By Putting known Values in the Formula for Cuboid-:

• $\longrightarrow {\mathrm {Volume= 7 \times 5 \times 8 }}$

• $\longrightarrow {\mathrm {Volume= 35 \times 8 }}$

• $\longrightarrow {\mathrm {Volume= 280cm^{3} }}$

Therefore,

• $\underline{\boxed {\mathrm {\dag{Volume\:of\:Cuboid\:= 280cm^{3} }}}}$

Volume of Cube -:

As , We know that ,

• $\underline {\boxed{\dag{\red{\mathrm{ Volume_{(\:Cube)} = Edge \times Edge \times Edge \:cubic.m}}}}}$

Here ,

• Edge of Cube-: 8 cm

Now By Putting known Values in Formula for Volume of Cube-:

• $\longrightarrow {\mathrm {Volume= 8 \times 8 \times 8 }}$

• $\longrightarrow {\mathrm {Volume= 64 \times 8 }}$

• $\longrightarrow {\mathrm {Volume= 512cm^{3} }}$

Therefore,

• $\underline{\boxed {\mathrm {\dag{Volume\:of\:Cube\:= 512cm^{3} }}}}$

Now , By Comparing Volume of Cube to Volume of cuboid -:

Here,

• $\longrightarrow {\mathrm {Volume\:of\:Cube= 512cm^{3} }}$

• $\longrightarrow {\mathrm {Volume\:of\:Cuboid = 280cm^{3} }}$

We can see that ,

• [ 512 cm³ > 280 cm³]

Or ,

• [ Volume of Cube > Volume of Cuboid]

Or ,

• $\underline{\boxed {\mathrm {\dag{Volume\:of\:Cube\:is\: greater\:than\:Volume\:of\:Cuboid }}}}$

Hence ,

• $\underline{\boxed {\mathrm {\dag{\red{Volume\:of\:Cube\:is\: greater\:than\:Volume\:of\:Cuboid }}}}}$

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