Question

what is the volume of a cube whose total surface area is 864 cm2​

Answer 1

Given :

• Total surface area of cube is 864 cm².

To Find :

• The volume of cube = ?

Solition :

★ First of all find the sides of the cube :

→ TSA of a cube = 6 × (Side)²

→ 864 = 6 × (Side)²

→ 864 ÷ 6 = (Side)²

→ 144 = (Side)²

→ (Side)² = 144

→ Side = √144

→ Side = 12 cm

• Hence,the side of cube is 12 cm.

Verification :

→ 864 = 6 × (Side)²

→ 864 = 6 × (12)²

→ 864 = 6 × 144

→ 864 = 864

Hence, Verified !

★ Now, let's find the volume of cube :

→ Volume of cube = (Side)³

→ Volume of cube = (12)³

→ Volume of cube = 1728 cm³

• Hence,the volume of cube is 1728 cm³.

★ Formulas related to cube and cuboid :

• Volume of cuboid = l × b × h
• C.S.A of cuboid = 2(l + b)h
• T.S.A of cuboid = 2(lb + bh + lh)
• C.S.A of cube = 4a²
• T.S.A of cube = 6a²
• Volume of cube = a³