Question

Surface area of a cube is 150 cm² . then find the volume of this cube.

Answer 1

$\Large{\underline{\underline{\mathfrak{\red{\bf{Solution}}}}}}$

$\Large{\underline{\mathfrak{\orange{\bf{Given}}}}}$

• Surface area of cube = 150 cm²

$\Large{\underline{\mathfrak{\orange{\bf{Find}}}}}$

• Volume of cube

$\Large{\underline{\underline{\mathfrak{\red{\bf{Explanation}}}}}}$

Let,

• Side of cube be = x cm

Using Formula

$\small{\boxed{\boxed{\green{\tt{\:Surface\:Area_{cube}\:=\:6(side)^2}}}}}$

$\small{\boxed{\boxed{\blue{\tt{\:Volume_{cube}\:=\:(side)^³}}}}}$

Now, calculate side of cube

➡Surface area of cube = 6(side)²

keep value of surface area

➡ 150 = 6x²

➡x² = 150/6

➡x² = 25

➡x = ±√25

➡x = ±√(5×5)

➡x = ± 5

Side be always positive ,

so neglect -5 , And take +5

So,

• x = 5 cm

Now, calculate , Volume of cube

➡ Volume of cube = (side)³

Keep value of side

➡ Volume of cube = (5)³

➡ Volume of cube = 5 × 5 × 5

➡ Volume of cube = 125 cm³

$\Large{\underline{\underline{\mathfrak{\red{\bf{Hence}}}}}}$

• Volume of cube will be = 125 cm³

_________________

Answer 2

Step-by-step explanation:

V≈125cm³

A Surface area 150cm²

Using the formulas

A = 6a²

V = a³

Solving for V

V=√6/A⅔36 = √6·150⅔/36 ≈ 125cm³