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.
Answers
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:
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: