the total surface of the area of a cube is 1350 sq.m . find the volume​

2 thoughts on “the total surface of the area of a cube is 1350 sq.m . find the volume​”

1. To Find :–

   • The volume of the cube

   Solution:

   Given that,

   • The total surface area of cube = 1350m²

   We know that,

   Total surface of cube = 6(a)² sq. units,

   ∴ The side of cube is :-

   ⟶ 6(a)² = 1350

   ⟶ a² = 1350 ÷ 6

   ⟶ a² = 225

   ⟶ a² = 15 × 15

   ⟶ a = 15m

   Hence,

   The volume of cube :-

   We know that,

   Volume of cube = (a)³ cubic units,

   ∴ The volume of cube is :-

   ⟶ Volume = (a)³

   ⟶ Volume = (15)³

   ⟶ Volume = ( 15 × 15 × 15 )m²

   ⟶ Volume = 3375m²

   Required Answer :-

   • The volume of cube is 3375m².

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2. Given :

   • Shape = Cube
   • Total Surface Area of Cube = 1350m²

   [tex] \\ [/tex]

   To Find :

   • Volume of Cube

   [tex] \\ [/tex]

   Solution :

   ✰ As we know that, Total Surface Area (TSA) of cube is given by 6 × (side)² . For finding the volume of cube we need the side of cube as volume of cube is given by (side)³ . Now, we will find the side of the cube by applying the formula of Total Surface Area of cube.

   ⠀⠀

   ⟹ Total Surface Area = 6 × (side)²

   ⟹ 1350 = 6 × (side)²

   ⟹ 1350 / 6 = (side)²

   ⟹ 225 = (side)²

   ⟹ √225 = side

   ⟹ 15 = side

   ⠀

   Now,

   ➟ Volume of Cube = (side)³

   ➟ Volume of Cube = (15)³

   ➟ Volume of Cube = 15 × 15 × 15

   ➟ Volume of Cube = 225 × 15

   ➟ Volume of Cube = 3375m³

   Thus Volume of Cube is 3375m³

   ________________

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