Answer:
4. 16 times longer
5. 4 times longer
6. 64 times longer
Step-by-step explanation:
Solving (4):
Let the length and with of the object be x and y
[tex]Area_1 = x * y[/tex]
Apply Scale Factor of 4
[tex]New\ length = 4 * x[/tex]
[tex]New\ length = 4x[/tex]
[tex]New\ Width = 4 * y[/tex]
[tex]New\ Width = 4y[/tex]
[tex]Area_2 = 4x * 4y[/tex]
[tex]Area_2 = 16xy[/tex]
Divide Area₂ by Area₁
[tex]Ratio = \frac{16xy}{xy}[/tex]
[tex]Ratio = 16[/tex]
Hence;
The surface area will increase 16 times longer
Solving (5):
Let the length and with of the object be x and y
[tex]Area_1 = x * y[/tex]
When the object is increased by a scale factor of 4;
It means that the Area is increased by a scale factor of 4
i.e.
[tex]Area_2 = 4 * Area_1[/tex]
[tex]Area_2 = 4Area_1[/tex]
Divide Area₂ by Area₁
[tex]Ratio = \frac{Area_2}{Area_1}[/tex]
[tex]Ratio = \frac{4Area_1}{Area_1}[/tex]
[tex]Ratio = 4[/tex]
Hence;
The surface area will increase 4 times longer
Solving (6):
Let the length, width and height of the object be x, y and z
[tex]Volume_1 = x * y * z[/tex]
[tex]Volume_1 = x y z[/tex]
Apply Scale Factor of 4
[tex]New\ length = 4 * x[/tex]
[tex]New\ length = 4x[/tex]
[tex]New\ Width = 4 * y[/tex]
[tex]New\ Width = 4y[/tex]
[tex]New\ Height = 4 * z[/tex]
[tex]New\ Height = 4 z[/tex]
[tex]Volume_2 =4 x *4 y * 4z[/tex]
[tex]Volume_2 = 64x y z[/tex]
Divide Volume₂ by Volume₁
[tex]Ratio = \frac{64xyz}{xyz}[/tex]
[tex]Ratio = 64[/tex]
Hence;
The volume will increase by 64 times
