If each edge of a cube in doubled. (a) how mony times will its surface area increase ?
(b) how many times will its volume increase ?
Answers
Answer:
a) Four times
b) Eight times
Step-by-step explanation:
Given-----> Each edge of cube is doubled
To find----->
a) How many times wii its surface area increase
b) how many times will its volume increase
Solution-----> Let initially edge of cube be x
Surface area of cube ( S₁ ) = 6 ( edge )²
S₁ = 6 ( x )²
S₁ = 6 x²
Volume of cube ( V₁ ) = edge³
V₁ = x³
Now , edge of cube is doubled so,
Edge of new cube = 2x
Now , surface area of new cube ( S₂ )
= 6 ( new edge )²
S₂ = 6 ( 2x )²
= 6 ( 4x² )
S₂ = 24 x²
Volume of new cube = ( New edge )³
V₂ = ( 2x )³
V₂ = 8x³
a) S₂ = 24x²
= 4 ( 6x² )
S₂ = 4 ( S₁ )
It means surface area increase four times .
b) V₂ = 8x³
V₂ = 8 ( V₁ )
It means volume is increased eight times .