What is the volume of a rectangular solid, the width of which is equal to a cm, the length is twice the width and the height is twice the length?

the width is equal to a cm.

the length is twice the width, therefore the length is equal to 2a cm.

the height is twice the length, therefore the height is equal to 4a cm.  

the volume is equal to width times length times height which is equal to a * 2a * 4a which is equal to 8a^3 cubic cm.  

For Example:

let a = 5

then 2a = 10

then 4a = 20  

a is the width

2a is the length

4a is the height.  

the length is twice the width.

the height is twice the length  

the volume is equal to a * 2a * 4a which is equal to 8a^3 cubic cm.  

this is equivalent to 8 * 5^3 which is equal to 8 * 125 which is equal to 1000 cubic cm.  

5 * 10 * 20 = 50 * 20 = 1000 cubic cm.  

formula works and so is considered to be good.  

the volume is equal to 8a^3 cubic cm.

* hope you understand*

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!

(-5,-28)

i graphed to on desmos.