Geometry Questions!

[flash36]

Please help me with these if you can.

Calculate the unknown dimensions, given the total surface area of the objects. Give answers to 1 decimal place.

a Length of a cube with a total surface area of 24 m2

b The radius of a sphere with a total surface area of 633.5 cm2

c Length of a cuboid with width of 12 mm, height of 6 cm and a total surface area of 468 cm2

d Diameter of a playing ball with a total surface area of 157 630 cm2

Also...

Scale factor, k, is the amount of enlargement or reduction and is expressed as integers, fractions or scale ratios; for example, k = 2, k = 1over12 or 1:10 000. - I don't understand this. How do you convetr ratios to scale factors?

Thanks!

[brightsky]

1. Total surface area of cube = , where is the length of the cube.

Hence

2. Total surface area of a sphere is given by: , where is the radius.

So

3. Total surface area of cuboid = where are the length, width and height respectively.

So

4. Total surface area of a sphere = , where is the radius.

So

Because the diameter is , hence the diameter is:



For the last question, in a ratio like 1:10000, where its x:y, it can be expressed as y = 10000x, and hence the scale factor of y to x is 10,000. You can do this for ratios like 2:3, which converted to algebraic form, is 2y = 3x, which can be simplified to y = 3x/2, so the scale factor is 3/2.

[flash36]

Thanks heaps!