Theresa and Angel are debating whether snow cones or ice cream cones are a greater value. One snow cone can be purchased for the same price as one ice cream cone, but Angel argues that the snow cone is better since it has a greater density than the ice cream cone. Both cones have a radius of 1.5 inches and a height of 3 inches, and the snow cone and ice cream cone weigh 4 ounces and 6 ounces, respectively. Assuming that the cones are filled precisely with no overflow, is Angel correct? Explain, rounding values to the nearest tenth of an ounce per cubic inch
A) Angel is correct since the density of the snow cone is 1.8 ounces per cubic inch, while the density of the ice cream cone is 1.2 ounces per cubic inch
B) Angel is correct since the density of the snow cone is 1.2 ounces per cubic inch, while the density of the ice cream cone is 0.8 ounces per cubic inch.
C) Angel is not correct since the density of the snow cone is 0.8 ounces per cubic inch, while the density of the ice cream cone is 1.3 ounces per cubic inch.
D) Angel is not correct since the density of the snow cone is 0.6 ounces per cubic inch, while the density of the ice cream cone is 0.8 ounces per cubic inch.
The correct answer is C) Angel is not correct since the density of the snow cone is 0.8 ounces per cubic inch, while the density of the ice cream cone is 1.3 ounces per cubic inch.
To find the density of each cone, we first need to calculate the volume of each cone. The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
For both cones:
V = (1/3)π(1.5)^2(3) = 3.5π cubic inches
Now, to find the density, we use the formula Density = mass/volume.
For the snow cone:
Density = 4 ounces / 3.5π cubic inches ≈ 0.8 ounces per cubic inch
For the ice cream cone:
Density = 6 ounces / 3.5π cubic inches ≈ 1.3 ounces per cubic inch
Therefore, Angel is not correct, as the density of the ice cream cone is greater than the density of the snow cone.
is that correct?
Apologies for the error in my calculations. Let's correct it.
Given:
Radius (r) = 1.5 inches
Height (h) = 3 inches
Snow cone weight = 4 ounces
Ice cream cone weight = 6 ounces
Volume of a cone (V) = (1/3)πr^2h
For both cones:
V = (1/3)π(1.5)^2(3) = 7.5π cubic inches
Density = mass/volume
For the snow cone:
Density = 4 ounces / 7.5π cubic inches ≈ 0.17 ounces per cubic inch
For the ice cream cone:
Density = 6 ounces / 7.5π cubic inches ≈ 0.25 ounces per cubic inch
Therefore, the correct answer is actually that Angel is correct since the density of the snow cone is 0.17 ounces per cubic inch, while the density of the ice cream cone is 0.25 ounces per cubic inch. Snow cones are indeed denser than ice cream cones in this case.
is that correct?
I apologize for my previous mistake. Let's reevaluate the calculations:
Given:
Radius (r) = 1.5 inches
Height (h) = 3 inches
Snow cone weight = 4 ounces
Ice cream cone weight = 6 ounces
Volume of a cone (V) = (1/3)πr^2h
For both cones:
V = (1/3)π(1.5)^2(3) = 7.5π cubic inches
Density = mass/volume
For the snow cone:
Density = 4 ounces / 7.5π cubic inches ≈ 0.17 ounces per cubic inch
For the ice cream cone:
Density = 6 ounces / 7.5π cubic inches ≈ 0.25 ounces per cubic inch
Therefore, the correct answer is actually that Angel is correct since the density of the snow cone is approximately 0.17 ounces per cubic inch, while the density of the ice cream cone is approximately 0.25 ounces per cubic inch. Snow cones are denser than ice cream cones in this case.