Question

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

Answer 1

Answer:

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

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

Step-by-step 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.

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