Question

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

by?
a.
4 times longer
64 times longer
b. 16 times longer
d. 8 times longer
5. If you increase an object by a scale factor of 4, how much longer would the object be?
a.
64 times longer
c.
8 times longer
b.
16 times longer
d.
4 times longer
6. If you increase all dimensions of an object by a scale factor of 4, how much would the volume increa
a.
4 times longer
c.
8 times longer
b.
64 times longer
d.
16 times longer
No

Answer 1

4. 16 times longer

5. 4 times longer

6. 64 times longer

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 = (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 = (Area_2)/(Area_1)`

`Ratio = (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 = (64xyz)/(xyz)`

`Ratio = 64`

Hence;

The volume will increase by 64 times