Question

39. (PISA): A goldsmith has a cubical shape gold biscuit of side 12cm.
He wants to sell to 8 different persons by converting it into 8 small cubes for those who
place order. What will be the side of the new cube. Find the ratio between surface areas of original and new
small cube.​

Answer 1

Answer:

Side of the cube = 12 cm

Volume of the cube = 1728 cm³

Volume of each smaller cube = 1728/8 cm³

                                                 = 216 cm³

Side of the new cube = ∛216 cm³

                                    = 6 cm

TSA of larger cube = 6 x 12 x 12 cm²

                                = 864 cm²

TSA of smaller cube = 6 x 6 x 6 cm²

                                  = 216 cm²

Ratio--

⇒ TSA of larger cube/ TSA of smaller cube

⇒ 864/216

⇒ 4 : 1

Hence the ratio of TSA of original cube to smaller cube is 4 : 1.

Answer 2

Answer:

side = 12

volume=a^3

∴12×12×12=1728

volume of new cube =a^3

since 8 cubes are formed

1728=8×a^3

∴a^3=216

a=6

surface are of large cube=6a^2=6×144 =864

surface area of smaller cube = 6×a^2 = 6× 216= 216

∴ratio= 864/216 = 4/1

 ∴4:1

Step-by-step explanation: