A solid cube is cut into 8 cubes of equal volumes. Find the ratio of the total surface area of the given cube and that of 1 smaller cube.
Let 'a' be edge of the original cube.
When it is cut into 8 cubes of equal volumes, Volume of each cube will be a3/8
Let A be edge of each new cube.
A3 = a3/8
A3 = (a/2)3
A = a/2 ...(i)
Ratio of TSA of given cube to 1 smaller cube = 6a2 / 6A2
= a2 / (a/2)2
= a2 / (a2/4)
= 4a2 / a2
= 4/1
= 4:1
When it is cut into 8 cubes of equal volumes, Volume of each cube will be a3/8
Let A be edge of each new cube.
A3 = a3/8
A3 = (a/2)3
A = a/2 ...(i)
Ratio of TSA of given cube to 1 smaller cube = 6a2 / 6A2
= a2 / (a/2)2
= a2 / (a2/4)
= 4a2 / a2
= 4/1
= 4:1