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

Find the volume of the shaded figure by subtracting

janiyaf8941

01.02.2022

a. 9a^3 - 9ab^2

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

Step-by-step explanation:

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)

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