Question

A cubical cake of side 16 cm is cut into 8 cubes of equal volume. What will be the side of the new cube? Also find the ratio between their surface areas.​

Answer 1

Given data : A cubical cake of side 16 cm is cut into 8 cubes of equal volume.

• cubical side of cake = 16 cm
• volume of cake = ?

Solution :

Firstly we have to find volume of cubical cake.

⟹ volume of cubical cake = (side)³

⟹ volume of cubical cake = 16³

⟹ volume of cubical cake = 4096 cm³ ----{1}

Now,

⟹ surface area of cubical cake = 6 * (side)²

⟹ surface area of cubical cake = 6 * (16)²

⟹ surface area of cubical cake = 6 * 256

⟹ surface area of cubical cake = 1536 cm² ----{2}

Here, we know that cubical cake is cut into 8 cubes of equal volume.

Now,

⟹ volume of new cubical cakes = 4096/8

⟹ volume of new cubical cakes = 512 cm³

Now, to find side of new cubical cakes .

⟹ volume of new cubical cakes = (side)³

⟹ 512 = (side)³

⟹ side = ³√512

⟹ side = 8 cm

Now,

⟹ surface area of new cubical cakes = 1536/8

⟹ surface area of new cubical cakes = 192 cm²

Now,

⟹ surface area of cubical cake : surface area of new cubical cake = 1536 : 192

⟹ surface area of cubical cake : surface area of new cubical cake = 8 : 1

Answer : The side of the new cubical cake is 8 cm and ratio of surface area of cubical cake to new cubical cake is 8 : 1.