Question

the lateral surface area of a cube is 10 cm square find its volume.
ans=125
solve the equation ​

Answer 1

Answer:

$\blue\bigstar$ Volume of the cube = 3.375 cm³ ≈ 3.38 cm³.

SOLUTION

Lateral Surface area (LSA) of a cube = 10cm².

Lateral Surface area (LSA) of a cube = 4a², Where a is the side of the cube .

Here,

Lateral Surface area(LSA) is given as 10cm².

$\implies$ 4a² = 10

$\implies \sf a^2 = \dfrac{10}{4}$

$\implies$ a² = 2.5

∵ a² = 2.5

$\sf a = \sqrt{2.5}$

$\implies \sf a =\sqrt{2.5} = 1.581 cm.$

Side of the cube (a) = 1.581 ≈ 1.5 cm

$\setlength{\unitlength}{4mm}\begin{picture}(10,6)\thicklines\put(0,1){\line(0,1){10}}\put(0,1){\line(1,0){10}}\put(10,1){\line(0,1){10}}\put(0,11){\line(1,0){10}}\put(0,11){\line(1,1){5}}\put(10,11){\line(1,1){5}}\put(10,1){\line(1,1){5}}\put(0,1){\line(1,1){5}}\put(5,6){\line(1,0){10}}\put(5,6){\line(0,1){10}}\put(5,16){\line(1,0){10}}\put(15,6){\line(0,1){10}}\put(4.6,-0.5){\bf\large 1.5cm}\put(13.5,3){\bf\large 1.5cm}\put(-4,5.8){\bf\large 1.5cm}\end{picture}$

Volume of a cube = a³ , Where a is the side of the cube .

$\implies$ Volume of the cube = (1.5)³

$\implies$ Volume of the cube = 3.375 cm³.

Answer 2

Question:

$\:\:\:\:\:\:\:$

$\to$ The Lateral surface area of a cube is 10$\rm\bold{\:cm^2}$.Find its volume.

$\:\:\:\:\:\:\:$

To Find:

$\:\:\:\:\:\:\:$

• Find the volume of the cube ?

$\:\:\:\:\:\:\:$

Given:

$\:\:\:\:\:\:\:$

• Lateral surface area of a cube is 10$\rm\bold{\:cm^2}$

$\:\:\:\:\:\:\:$

Required Formula:

$\:\:\:\:\:\:\:$

• Lateral surface area of a cube = 4 $\rm{a^2}$
• Volume of the cube = $\rm{ {a}^{3} }$

$\:\:\:\:\:\:\:$

Solution:

$\:\:\:\:\:\:\:$

Lateral surface area of a cube = 10 cm

$\to \sf{4 {a}^{2} = 10}$

$\to \sf{ {a}^{2} = \cancel \frac{10}{4} }$

$\to \sf{ {a}^{2} = 2.5}$

$\to \sf{a = \sqrt{2.5} }$

$\to \sf{a = 1.5}$

Let us assume that,

• a = 1.5 cm

$\to \sf{ {a}^{3} = 1.5^{3}}$

$\to \sf{{a}^{3} = 3.375 {cm}^{3} }$