Question

if the diagonal of a cube is 2.5m then volume is --------------- m cube​

Answer 1

Step-by-step explanation:

Volume of cube is a^3

Therefore the answer would be=(2.5)^3

That is=15.625

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Answer 2

» Question :

if the diagonal of a cube is 2.5m, then volume is cube (in m) is ?

» To Find :

The volume of the cube.

» We Know :

Formula for Body Diagonal of a Cube :

$\sf{\underline{\boxed{D_{c} = \sqrt{a^{2} + a^{2} + a^{2}}}}}$

Formula for volume of a Cube :

$\sf{\underline{\boxed{V_{c} = a^{3}}}}$

Where , a is the side of the cube.

» Concept :

By the value of given diagonal ,we can calculate the lenth of the side ,by using the formula for the Length of the Diagonal of a Cube.

Given Formula :

$\sf{\underline{\boxed{D_{c} = \sqrt{a^{2} + a^{2} + a^{2}}}}}$

Now by further calculation ,we get the formula for a diagonal as :

$\sf{\underline{\boxed{\therefore D_{c} = \sqrt{3}a}}}$

Now ,by putting the value of Diagonal in the formula ,we can find the length of the side.

» Solution :

Side of the cube :

• Diagonal = 2.5 m

Formula :

$\sf{\underline{\boxed{D_{c} = \sqrt{3}a}}}$

By substituting the value,we get :

$\sf{\Rightarrow 2.5 = \sqrt{3}a}$

$\sf{\Rightarrow \dfrac{2.5}{\sqrt{3}} = a}$

$\sf{\Rightarrow \cancel{\dfrac{2.5}{\sqrt{3}}} = a}$

$\sf{\Rightarrow 1.44 m = a}$

Hence ,the lenth of the edge is 1.44 m.

Volume of the cube :

• Edge = 1.44 m

Formula :

$\sf{\underline{\boxed{V_{c} = a^{3}}}}$

By substituting the value,we get :

$\sf{\Rightarrow V_{c} = 1.44^{3}}$

$\sf{\Rightarrow V_{c} = 1.44 \times 1.44 \times 1.44}$

$\sf{\Rightarrow V_{c} = 2.98(approx.) m^{3}}$

Hence ,the volume of the cube is 2.98 m³.

Additional information :

• Area of a Rectangle = length × breadth

• Area of a Square = (side)²

• Surface area of a Cube = 6(a)²

• Lateral surface area of a Cube = 4(a)²