Question

4. If you increase all dimensions of an object by a scale factor of 4, how much would the surface area i

Answer 1

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

$Area_1 = x * y$

Apply Scale Factor of 4

$New\ length = 4 * x$

$New\ length = 4x$

$New\ Width = 4 * y$

$New\ Width = 4y$

$Area_2 = 4x * 4y$

$Area_2 = 16xy$

Divide Area₂ by Area₁

$Ratio = \frac{16xy}{xy}$

$Ratio = 16$

Hence;

The surface area will increase 16 times longer

Solving (5):

Let the length and with of the object be x and y

$Area_1 = x * y$

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.

$Area_2 = 4 * Area_1$

$Area_2 = 4Area_1$

Divide Area₂ by Area₁

$Ratio = \frac{Area_2}{Area_1}$

$Ratio = \frac{4Area_1}{Area_1}$

$Ratio = 4$

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

$Volume_1 = x * y * z$

$Volume_1 = x y z$

Apply Scale Factor of 4

$New\ length = 4 * x$

$New\ length = 4x$

$New\ Width = 4 * y$

$New\ Width = 4y$

$New\ Height = 4 * z$

$New\ Height = 4 z$

$Volume_2 =4 x *4 y * 4z$

$Volume_2 = 64x y z$

Divide Volume₂ by Volume₁

$Ratio = \frac{64xyz}{xyz}$

$Ratio = 64$

Hence;

The volume will increase by 64 times