Question

Find the volume of the shaded figure by subtracting the smaller volume from the larger

Answer 1

a.
`9a^3 - 9ab^2`

b.
`9a(a^2 - b^2)`

Explanation:

a.

`Volume = l*w*h`

`Volume_(smaller) = l*w*h`

Where,
`l = 9a, w = b, h = b`

`Volume_(smaller) = 9a*b*b = 9ab^2`

`Volume_(larger) = l*w*h`

Where,
`l = 9a, w = a, h = a`

`Volume_(smaller) = 9a*a*a = 9a^3`

Volume of the shaded figure =
`9a^3 - 9ab^2`

b.
`9a^3 - 9ab^2` expressed in factored form:

Look for the term that is common to 9a³ and 9ab², then take outside the parenthesis.

`9a^3 - 9ab^2 = 9a(a^2 - b^2)`