Question

A solid with volume 8 cubic units is dilated by a scale factor of k to obtain a solid with volume V cubic units. Find the value of k which results in an image with each given volume.

a. 216 cubic units

k=

b. 1 cubic unit

k=

c. 1,000 cubic units

k=

Answer 1

a. k = 27

b. k = 216

c. k = 0.216

Explanation:

The value of the scale factor can be given by the following formula:

`k = (Final\ Volume)/(Initial\ Volume)`

where,

Initial Volume = 8 cubic units

a.

Final Volume = 216 cubic units

Therefore,

`k = (216\ cubic\ units)/(8\ cubic\ units)`

k = 27

b.

Final Volume = 1 cubic units

Therefore,

`k = (216\ cubic\ units)/(1\ cubic\ units)`

k = 216

c.

Final Volume = 1000 cubic units

Therefore,

`k = (216\ cubic\ units)/(1000\ cubic\ units)`

k = 0.216