Question

The formula for the volume of a right circular cylinder is V = πr² h. If r = 2b and

h=5b+3, what is the volume of the cylinder in terms of b?

Answer 1

`V=4\pi b^(2)(5b+3)`.

Explanation:

1. Write the equation.

`V=\pi r^(2) h`

2. Use the values to substitute into the original formula.

`V=\pi r^(2) h\\ \\V=\pi (2b)^(2) (5b+3)`

3. Solve the exponent.

`V=\pi (2^(2) b^(2) ) (5b+3)\\ \\V=\pi (4 b^(2) ) (5b+3)`

4. Solve the product between the two parentheses and simplify.

Use the distributive property of multiplication in order to operate.

`V=\pi (4 b^(2) ) (5b+3)\\ \\V=\pi ((4 b^(2))(5b)+(4 b^(2))(3))\\ \\V=\pi ((20b^(3) )+(12 b^(2)))\\ \\V=4\pi (\frac{20b^(3)}4} +(12 b^(2))/(4) )\\ \\V=4\pi (5b^(3) +3b^(2))\\ \\V=4\pi b^(2)((5b^(3))/(b^(2)) +(3b^(2))/(b^(2)) )\\ \\V=4\pi b^(2)(5b+3)`

5. Conclude.

`V=4\pi b^(2)(5b+3)`.