Put the cones in order from greatest volume to least volume.
Try to put them in order thinking about the formula instead of actually solving for the volume.
(5 points)
Cone 1 radius 3cm height 8cm
cone 2 radius 9cm height 12cm
cone 3 radius 3cm height 21cm
cone 4 radius 8cm height 18cm
cone 5 radius 5cm height 13cm
1. Cone 2 (radius 9cm, height 12cm) - the largest volume since it has the largest radius and height.
2. Cone 4 (radius 8cm, height 18cm) - the second largest volume since it has a larger height compared to cone 2.
3. Cone 5 (radius 5cm, height 13cm) - the third largest volume since it has a smaller radius but larger height compared to cone 1.
4. Cone 1 (radius 3cm, height 8cm) - the second smallest volume since it has the smallest radius and height.
5. Cone 3 (radius 3cm, height 21cm) - the smallest volume since it has the smallest radius but largest height.
Are you sure explain each one
1. Cone 2 (radius 9cm, height 12cm) has the largest volume because it has the largest radius and height among all the cones. The formula for the volume of a cone is V = (1/3)πr^2h, so in this case, both the radius and height contribute to a larger volume compared to the other cones.
2. Cone 4 (radius 8cm, height 18cm) has the second largest volume because it has a larger height compared to Cone 2, even though the radius is slightly smaller. The height plays an important role in determining the volume of a cone.
3. Cone 5 (radius 5cm, height 13cm) has the third largest volume because even though the radius is smaller than Cone 2 and 4, the height is larger than Cone 1 which contributes to a larger volume.
4. Cone 1 (radius 3cm, height 8cm) has the second smallest volume because both the radius and height are smaller compared to the other cones, resulting in a smaller volume.
5. Cone 3 (radius 3cm, height 21cm) has the smallest volume because even though the height is the largest among all the cones, the radius is the smallest which significantly affects the volume of the cone.
Okay now solve each one and answer the question again
Let's calculate the volume of each cone using the formula V = (1/3)πr^2h:
1. Cone 1:
V = (1/3) * π * 3^2 * 8
V = (1/3) * π * 9 * 8
V = 24π cubic cm
2. Cone 2:
V = (1/3) * π * 9^2 * 12
V = (1/3) * π * 81 * 12
V = 324π cubic cm
3. Cone 3:
V = (1/3) * π * 3^2 * 21
V = (1/3) * π * 9 * 21
V = 63π cubic cm
4. Cone 4:
V = (1/3) * π * 8^2 * 18
V = (1/3) * π * 64 * 18
V = 384π cubic cm
5. Cone 5:
V = (1/3) * π * 5^2 * 13
V = (1/3) * π * 25 * 13
V = 325π cubic cm
Now, in order from greatest volume to least volume:
1. Cone 4 (384π cubic cm)
2. Cone 2 (324π cubic cm)
3. Cone 5 (325π cubic cm)
4. Cone 3 (63π cubic cm)
5. Cone 1 (24π cubic cm)
Therefore, the cones in order from greatest volume to least volume are: Cone 4, Cone 2, Cone 5, Cone 3, Cone 1.