Answer:
\(V = 50\pi x^3+240\pi x^2+168\pi x+32 \pi\)
Step-by-step explanation:
Volume of cylinder(V) is given by:
\(V = \pi r^2h\)
where,
r is the radius of the cylinder
h is the height of the cylinder.
As per the statement:
A cylinder has a radius of 5x + 2 and a height of 2x + 8
⇒r = 5x +2 units and h = 2x+8 units
Substitute in [1] we have;
\(V = \pi (5x+2)^2 \cdot (2x+8)\)
Using the identity rule:
\((a+b)^2 = a^2+b^2+2ab\)
⇒\(V = \pi (25x^2+4+20x)(2x+8)\)
⇒\(V = \pi (50x^3+8x+40x^2+200x^2+32+160x)\)
Combine like terms;
⇒\(V = \pi (50x^3+240x^2+168x+32)\)
⇒\(V = 50x^3 \pi+240x^2 \pi+168x \pi+32 \pi\)
Therefore, in standard form best describes the total volume of the cylinder is: \(V = 50x^3 \pi+240x^2 \pi+168x \pi+32 \pi\)
