Question

Question

Order the cylinders from greatest volume (put at the top of the list) to least volume (put at the bottom of the list).
The image shows three cylinders labeled A, B, and C with different dimensions. Cylinder A has a radius of r and a height of h. Cylinder B has a radius of 2r and the same height h as cylinder A. Cylinder C has the same radius r as cylinder A but a height of 3h. These cylinders are likely used to illustrate or solve mathematical problems related to volume or surface area. The image is from a page titled "Digital SAT Math Problems and Solutions (Part - 104)".

(3 points)

Answer 1

To order the cylinders by volume, we need to use the formula for the volume of a cylinder, which is given by:

\[ V = \pi r^2 h \]

Now let’s calculate the volumes of each cylinder based on the given dimensions:

1. Cylinder A:

   • Radius = \( r \)
   • Height = \( h \)
   • Volume \( V_A = \pi r^2 h \)

2. Cylinder B:

   • Radius = \( 2r \)
   • Height = \( h \)
   • Volume \( V_B = \pi (2r)^2 h = \pi (4r^2) h = 4\pi r^2 h \)

3. Cylinder C:

   • Radius = \( r \)
   • Height = \( 3h \)
   • Volume \( V_C = \pi r^2 (3h) = 3\pi r^2 h \)

Now we can compare the volumes:

• Volume of Cylinder A: \( V_A = \pi r^2 h \)
• Volume of Cylinder B: \( V_B = 4\pi r^2 h \)
• Volume of Cylinder C: \( V_C = 3\pi r^2 h \)

Ordering them from greatest to least volume:

1. Cylinder B: \( 4\pi r^2 h \)
2. Cylinder C: \( 3\pi r^2 h \)
3. Cylinder A: \( \pi r^2 h \)

So the final order from greatest volume to least volume is:

1. Cylinder B
2. Cylinder C
3. Cylinder A