Please help me with the following:
The volume of a cylinder is found using the formula V=πr^2h,where r is the radius of the base and h is the height. The volume of a rectangular prism of the same width (2r) and height h, as the cylinder, is found by multiplying the area of the base (2r x 2r) by the height. What is the ratio of the volume of the cylinder to the volume of the prism?
A. π/2
B. πr^4h^2
C. πr^2/4h
D. π/4
I think the answer is D, but I am stuck between B,C, and D. Is D the correct answer?
Please help me by checking my answer. Any help will be greatly appreciated! :)
P.S. Please answer as soon as possible again! I also think this is going to be the last one to be checked so far.
D is correct.
the ratio is just
(πr^2h) / (2r)^2*h
πr^2h / 4r^2h
π/4
Okay, cool! Thank you Dr.Bob222!!!! :D
Thank you for the explanation on this problem Steve! I understand it completely!
Find the volume of the cylinder. Use 3.14 for pi
Diameter 34m
Height 27m
This is a work pad question
To find the ratio of the volume of the cylinder to the volume of the prism, we need to compare the formulas for both volumes.
The volume of the cylinder is given by V = πr^2h, where r is the radius of the base and h is the height.
The volume of the prism is given by V = base area x height, where the base area is (2r) x (2r) = 4r^2.
So, the volume of the prism is V = 4r^2 x h = 4r^2h.
Now, let's find the ratio of the volume of the cylinder to the volume of the prism:
Ratio = Volume of cylinder / Volume of prism
Ratio = (πr^2h) / (4r^2h)
Since the h terms cancel out, we are left with:
Ratio = πr^2 / (4r^2)
Simplifying further, we can cancel out the r^2 terms:
Ratio = π / 4
So, the correct answer is D. The ratio of the volume of the cylinder to the volume of the prism is π/4.
Therefore, your initial guess is correct! Well done!