Beth Kuhlman
Jan 24, 2025
Math help quick!?
A cylinder has a radius of (5x + 2) and a height of (2x + 8). Which polynomial in standard form best represents the total volume of the cylinder? Use the formula (V = \pi r^2 h) for the volume of a cylinder.
A) (100\pi x^4 + 800\pi x^3 + 2256\pi x^2 + 1408\pi x + 256\pi)
B) (50\pi x^3 + 240\pi x^2 + 168\pi x + 32\pi)
C) (20\pi x^3 + 168\pi x^2 + 384\pi x + 128\pi)
D) (10\pi x^2 + 44\pi x + 16\pi)
5 Answers
B is right:V = pi (2x + 8) (5x + 2)^2= pi (2x + 8) (25x^2 + 20x + 4)= pi (50x^3 + 40x^2 + 8x + 200x^2 + 160x + 32)= pi (50x^3 + 240x^2 + 168x + 32)= 50pi x^3 + 240pi x^2 + 168pi x + 32pi
Feb 21, 2025
This is pretty simple if you take it step by step. So first thing were going to do is suare 5x+2. Remember that you cant just square the 5 and 2 and get your answer. It would by a polynomial. You must do it like this:(5x+2)^2 which is basically (5x+2)(5x+2)So now you foil that and that would give you 25x^2+10x+10x+4 which simplifies to 25x^2+20x+4. Now lets get the height in there as well. (25x^2+20x+4)(2x+8)50x^3+200x^2+40x^2+160x+8x+32That simplifies to:50x^3+240x^2+168x+32Now when you multiply that to pi that would just multiply each number by pi so:50pi x^3 + 240pi x^2 + 168 pi x + 32piSo the correct answer would be :Drum roll please:………… BNow you could have just stopped working after you calculated the 50 because there is only one choice with 50 in the answer choices, but it is always good to complete it in case your teacher wants to see all the work. It gets kind of confusing when you simplify because of the x cubed and squared and just x all together so make sure you group them correctly or your answers will be all mixed up, and that won’t look good, especially if there was no multiple choice.
Feb 18, 2025
The previous answer is more thorough, but here’s the quick answer.You have to square 5x+2 and multiply that by 2x+8, and then multiply by pi. Look at the first term — you will get 25x^2 * 2x*pi = 50x^3pi.Only B has that term.
Volume of a cylinder is the area of the base times the height.We have the height and a radius, so we can compute the area, then determine the height.A = Ïr²A = Ï(5x + 2)²A = Ï(25x² + 20x + 4)Now that we have the area, multiply that by the height to get volumeV = AhV = Ï(25x² + 20x + 4)(2x + 8)V = Ï(50x³ + 200x² + 40x² + 160x + 8x + 32)V = Ï(50x³ + 240x² + 168x + 32)V = 50Ïx³ + 240Ïx² + 168Ïx + 32ÏThe answer is B.
Related Questions
Find the circumference of a circle with a radius of 5 inches. Please express your answer in terms of pi.
How tall is 77 inches when converted to feet?
In circle O, ST is a diameter. What is the value of x if (2x + 8) equals one of the following options: 22.0, 25.0, 25.4,...
I have a question regarding torque in a magnetism context. I understand that the equation τ = IABsin(θ) will be relevant...
Could you please help me find the cube roots of the complex number represented in polar form as 8(cos 216° + i sin 216°)...
Please find below the present and future values for different interest rates. Compounding and discounting occur annually...
A radio telescope features a parabolic surface, as illustrated below. Given that the telescope is 1 meter deep and 12 me...
What is the cube root of ( b^{27} )?
How many moles of CuO can be produced from 0.450 moles of Cu2O in the following reaction: 2Cu2O + O2 → 4CuO?
Suppose you are asked to calculate the area of a rectangle that is 2.1 cm wide and 5.6 cm long. Your calculator provides...