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.

Question

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 1.2 ounces per cubic inch, while the density of the ice cream cone is 0.8 ounces per cubic inch.

B) 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.

C) 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.

D) 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.

Answer 1

To determine the density of the snow cone and ice cream cone, we need to calculate their volumes first.

The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.

For both the snow cone and ice cream cone, the radius is 1.5 inches and the height is 3 inches.

V = (1/3) * π * 1.5^2 * 3
≈ 7.1 cubic inches

Now, we can calculate the density by dividing the weight by the volume.

For the snow cone, the weight is 4 ounces, so the density is 4/7.1 ≈ 0.6 ounces per cubic inch.

For the ice cream cone, the weight is 6 ounces, so the density is 6/7.1 ≈ 0.8 ounces per cubic inch.

Therefore, Angel is not correct. 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 0.6 ounces per cubic inch, while the density of the ice cream cone is 0.8 ounces per cubic inch.