Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Avery is measuring two cylinders. Given the volume V and the base radius r of the first cylinder, Avery uses the formula h=(V)/(pir^(2)) to compute its height h to be 24 centimeters. The second cylinder has the same volume, but has 2 times the radius. What is its height? Choose 1 answer: A 6 centimeters (B) 12 centimeters (C) 48 centimeters (D) 96 centimeters

Avery is measuring two cylinders.\newlineGiven the volume V V and the base radius r r of the first cylinder, Avery uses the formula\newlineh=Vπr2 h=\frac{V}{\pi r^{2}} \newlineto compute its height h h to be 2424 centimeters.\newlineThe second cylinder has the same volume, but has 22 times the radius. What is its height?\newlineChoose 11 answer:\newline(A) 66 centimeters\newline(B) 1212 centimeters\newline(C) 4848 centimeters\newline(D) 9696 centimeters

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Interpret parts of quadratic expressions: word problemsright chevron icon

Full solution

Q. Avery is measuring two cylinders.\newlineGiven the volume V V and the base radius r r of the first cylinder, Avery uses the formula\newlineh=Vπr2 h=\frac{V}{\pi r^{2}} \newlineto compute its height h h to be 2424 centimeters.\newlineThe second cylinder has the same volume, but has 22 times the radius. What is its height?\newlineChoose 11 answer:\newline(A) 66 centimeters\newline(B) 1212 centimeters\newline(C) 4848 centimeters\newline(D) 9696 centimeters
  1. Understanding the relationship: Understand the relationship between the volume of a cylinder and its dimensions.\newlineThe volume of a cylinder (VV) is given by the formula V=πr2hV = \pi r^2 h, where rr is the radius and hh is the height of the cylinder.
  2. Expressing the height of the first cylinder: Use the given formula to express the height of the first cylinder.\newlineThe height hh of the first cylinder is given by the formula h=V(πr2)h = \frac{V}{(\pi r^2)}. We are told that h=24h = 24 centimeters for the first cylinder.
  3. Calculating the radius of the first cylinder: Calculate the radius of the first cylinder.\newlineSince we know the height of the first cylinder, we can rearrange the formula to solve for the radius rr. However, we do not need to calculate the actual radius because the problem states that the second cylinder has twice the radius of the first. We can use the relationship between the radii of the two cylinders in the next step.
  4. Determining the relationship between the heights: Determine the relationship between the heights of the two cylinders.\newlineThe second cylinder has the same volume as the first but has twice the radius. Let's denote the radius of the second cylinder as r2=2r r_2 = 2r . The height of the second cylinder (h2 h_2 ) can be found using the same volume formula: h2=V(πr22) h_2 = \frac{V}{(\pi r_2^2)} .
  5. Substituting the radius of the second cylinder: Substitute the radius of the second cylinder into the formula.\newlineUsing the fact that r2=2rr_2 = 2r, we can substitute into the formula for h2h_2 to get h2=V(π(2r)2)=V(4πr2)h_2 = \frac{V}{(\pi(2r)^2)} = \frac{V}{(4\pi r^2)}.
  6. Comparing the formulas for h_2 and h: Compare the formula for h_2 with the formula for h.\newlineWe see that h_2 = \frac{V}{44\pi r^22} is one-fourth of h = \frac{V}{\pi r^22} because of the factor of 44 in the denominator due to the squared radius being four times larger for the second cylinder.
  7. Calculating the height of the second cylinder: Calculate the height of the second cylinder.\newlineSince the height of the first cylinder is 2424 centimeters, the height of the second cylinder will be one-fourth of that, because the volume is constant and the radius is doubled. Therefore, h2=24 cm4=6h_2 = \frac{24 \text{ cm}}{4} = 6 centimeters.

More problems from Interpret parts of quadratic expressions: word problems

Question
The function h h is defined over the real numbers. This table gives a few values of h h .\newline\begin{tabular}{lllll}\newlinex x & −6-6.11 & −6-6.0101 & −6-6.001001 & −5-5.99 \\\newline\hlineh(x) h(x) & −0-0.2525 & −0-0.7474 & −0-0.9898 & −1-1.00\newline\end{tabular}\newlineWhat is a reasonable estimate for lim⁡x→−6h(x) \lim _{x \rightarrow-6} h(x) ?\newlineChoose 11 answer:\newline(A) −6-6\newline(B) −2-2\newline(C) −1-1\newline(D) The limit doesn't exist
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the amplitude of\newlineg(x)=−2sin⁡(π2x−3)+5? g(x)=-2 \sin \left(\frac{\pi}{2} x-3\right)+5 ? \newlineunits
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the amplitude of y=5sin⁡(4x−2)−3 y=5 \sin (4 x-2)-3 ?\newlineunits
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the amplitude of y=−3cos⁡(πx+2)−6? y=-3 \cos (\pi x+2)-6 ? \newlineunits
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the amplitude of y=3sin⁡(2x−1)+4 y=3 \sin (2 x-1)+4 ?\newlineunits
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the period of the function h(x)=−3cos⁡(πx+2)−6? h(x)=-3 \cos (\pi x+2)-6 ? \newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the period of the function\newlineh(x)=5sin⁡(4x−2)−3 ?  h(x)=5 \sin (4 x-2)-3 \text { ? } \newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the period of the function g(x)=2cos⁡(7x+5)+1? g(x)=2 \cos (7 x+5)+1 ? \newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the period of the function f(x)=3sin⁡(2x−1)+4 f(x)=3 \sin (2 x-1)+4 ?\newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the period of the function f(x)=−4cos⁡(5x−9)−7 f(x)=-4 \cos (5 x-9)-7 ?\newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 10 months ago

View all (4)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant