Question

The surface area of a cube is 1734 sq. cm. Find the side of cube and its volume?

Answer 1

Let the side of the cube be x and we have Total Surface Area of cube as 1734 cm² then:-

$\\ \bullet \ {\underline{\underline{\boxed{\sf{ Total \ surface \ area _{(Cube)} = 6a^2 }}}}} \\ \\ \colon\implies{\sf{ 1734 = 6x^2 }} \\ \\ \colon\implies{\sf{ \cancel{ \dfrac{1734}{6} } = x^2 }} \\ \\ \colon\implies{\sf{ 289 = x^2 }} \\ \\ \colon\implies{\sf{ x = \sqrt{289} \mapsto 17 \ cm }}$

So, The side of the cube will be 17 cm.

Now, we can find the volume of the cube using formula of volume as:-

$\\ \bullet \ {\underline{\underline{\boxed{\sf{ Volume _{(Cube)} = a^3 }}}}} \\ \\ \colon\implies{\sf{ (17)^3 }} \\ \\ \colon\implies{\sf{ 17 \times 17 \times 17 }} \\ \\ \colon\implies{\green{\sf{ 4913 }}}$

Hence,

$\\ {\underline{\sf{ The \ volume \ of \ the \ cube \ will \ be \ 4913 \ cm^3. }}}$

Answer 2

Question :

• The surface area of cuboid 1734 cm². Find the side of cube and its volume.

✰ Given :

• T. S. A of cube = 1734 cm²

✰ To find :

• Side of cube
• Volume of cube.

✰ Formulae to remember :

• T. S. A of cube = 6(side)²
• Volume of cube = (side) ³

✰ Solution :

• Finding the side of cube :-

➛ T.S.A of cube = 6(side)²

➛ 1735 = 6(side)²

➛ 1735/6 = side²

➛ 289.16 = side²

➛ √2899.16 = side

➛ Side = 17 cm

• Finding the volume of cube :-

➛ Volume of cube = (side)³

➛ Volume = (17)³

➛ Volume = 4913 cm³

✰ Therefore,

• Side of cube = 17cm
• Volume of cube = 4913 cm³