Question

instructions
solve the following problem and select your answer from the choices given.

question

the formula for the volume of a right circular cylinder is ( v = pi r^2 h ). if ( r = 2b ) and ( h = 5b + 3 ), what is the volume of the cylinder in terms of ( b )?

( 10pi b^2 + 6pi b )

( 20pi b^3 + 12pi b^2 )

( 20pi^2 b^3 + 12pi^2 b^2 )

( 50pi b^3 + 20pi b^2 + 90pi b )

Explanation:

Step1: Substitute r into formula

V = π(2b)²h = π(4b²)h

Step2: Substitute h into expression

V = 4πb²(5b + 3)

Step3: Expand the product

V = 4πb²×5b + 4πb²×3 = 20πb³ + 12πb²

Answer:

20πb³ + 12πb²