Mayur is in charge of creating themed popcorn containers for a county fair. He plans on creating cylindrical and cone-shaped containers. Each cylindrical container, x, has a volume of 52 in3, and each cone-shaped container, y, has a volume of 26 in3. Both containers have a height of 5.5 in. The system of equations shown can be used to find the number of cylindrical and cone-shaped containers at each snack booth in the fair.
52x + 26y = 7150
x + y = 175
Given that the diameter of the cone-shaped containers is 4.25 in, find the slant height of the cone-shaped containers. Round your answer to the nearest tenth.
A. 7.0 in
B. 5.1 in
C. 5.9 in
D. 7.6 in
To find the slant height of the cone-shaped containers, we need to first find the radius of the cone. The diameter is given as 4.25 in, so the radius is half of that, which is 4.25 / 2 = 2.125 in.
Next, we can use the formula for the volume of a cone to find the slant height:
V = (1/3)πr^2h
26 = (1/3)π(2.125)^2h
26 = (1/3)π(4.515625)h
26 = 1.505h
h ≈ 17.2 in
So, the slant height of the cone-shaped containers is approximately 17.2 in. Since the options do not match this result, there may have been a mistake in the calculations.