Susie runs an ice cream stand that also sells snow cones served in paper cones.
The paper cones she usually uses have a diameter of 6 inches and a height of 2 inches, but her supplier is out of them.
As a replacement, she purchases paper cones with a diameter of 2 inches and a height of 6 inches. How do the volumes of the original and replacement cones compare?
The replacement cone has a greater volume than the original cone.
The replacement cone has a greater volume than the original cone.
The original cone has a greater volume than the replacement cone.
The original cone has a greater volume than the replacement cone.
The original cone holds 2 times the amount as the replacement cone.
The original cone holds 2 times the amount as the replacement cone.
The original and replacement cones have the same volume.
The original and replacement cones have the same volume.
The original cone has a greater volume than the replacement cone.
To calculate the volume of a cone, you can use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
For the original cone:
r = 3 inches (half of the diameter)
h = 2 inches
V = (1/3) * π * 3^2 * 2 = 6π cubic inches
For the replacement cone:
r = 1 inch (half of the diameter)
h = 6 inches
V = (1/3) * π * 1^2 * 6 = 2π cubic inches
Since 6π > 2π, the original cone has a greater volume than the replacement cone.
When fully inflated, a blue exercise ball has a diameter of 56 cm. A similar red exercise ball, when fully inflated, has a diameter of 76 cm. Which statement is true?(1 point)
Responses
The volume of the blue ball is about 1.5 times larger than the volume of the red ball.
The volume of the blue ball is about 1.5 times larger than the volume of the red ball.
The volume of the red ball is about 1.5 times larger than the volume of the blue ball.
The volume of the red ball is about 1.5 times larger than the volume of the blue ball.
The volume of the blue ball is about 2.5 times larger than the volume of the red ball.
The volume of the blue ball is about 2.5 times larger than the volume of the red ball.
The volume of the red ball is about 2.5 times larger than the volume of the blue ball.
The volume of the blue ball is about 1.5 times larger than the volume of the red ball.
To calculate the volume of a sphere, you can use the formula V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter is given, we need to divide it by 2 to get the radius.
For the blue ball:
r_blue = 56 cm / 2 = 28 cm
V_blue = (4/3) * π * 28^3 ≈ 87843.39 cubic cm
For the red ball:
r_red = 76 cm / 2 = 38 cm
V_red = (4/3) * π * 38^3 ≈ 96004.39 cubic cm
Calculating the ratio of the volume of the blue ball to the volume of the red ball, we get:
V_blue / V_red ≈ 87843.39 / 96004.39 ≈ 0.915
Therefore, the volume of the blue ball is about 1.5 times larger than the volume of the red ball (approximately 1/0.915 ≈ 1.5).