Answer:
The volume of the larger cone is 18.8 sq.inches more than the volume of the smaller cone.
Step-by-step explanation:
Height of smaller cone = 3.5 inches
Diameter of smaller cone = 3 inches
Radius of smaller cone = [tex]\frac{3}{2} = 1.5 inches[/tex]
Volume of smaller cone = [tex]\frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times 1.5^2 \times 3.5=8.25 inches ^2[/tex]
Height of larger cone = 5.1 inches
Diameter of larger cone = 4.5 inches
Radius of larger cone =[tex]\frac{4.5}{2}=2.25 inches[/tex]
Volume of larger cone =[tex]\frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times 2.25^2 \times 5.1 =27.048 inches^2[/tex]
Difference in volumes = 27.048-8.25=[tex]18.798 inches^2[/tex]
Difference in volumes to nearest tenth =[tex]18.8 inches^2[/tex]
So, the volume of the larger cone is 18.8 sq.inches more than the volume of the smaller cone.
The volume of the larger cone is about 18.8 cubic inches greater than the volume of the small cone
The volume of a cone is calculated as:
[tex]V = \frac 13 \pi (\frac{d}{2})^2h[/tex]
For the small cone, we have the following parameters:
So, the volume of the small cone is:
[tex]V_s = \frac 13 \pi \times (\frac{3}{2})^2 \times 3.5[/tex]
[tex]V_s = 8.2[/tex]
For the large cone, we have the following parameters:
So, the volume of the large cone is:
[tex]V_l = \frac 13 \pi \times (\frac{4.5}{2})^2 \times 5.1[/tex]
[tex]V_l = 27.0[/tex]
Calculate the difference of both volumes
[tex]d =27.0 - 8.2[/tex]
[tex]d =18.8[/tex]
Hence, the volume of the larger cone is about 18.8 cubic inches greater than the volume of the small cone
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