MATH SOLVE

3 months ago

Q:
# Arrange the cones in order from least volume to greatest volume. a cone with a diameter of 20 units and a height of 12 units a cone with a diameter of 18 units and a height of 10 units a cone with a radius of 10 units and a height of 9 units

Accepted Solution

A:

Answer-[tex]\boxed{\boxed{\text{Volume}_2<\text{Volume}_3<\text{Volume}_4<\text{Volume}_1}}[/tex]Solution-The volume of the cone is given by,[tex]\text{Volume}=\pi r^2\dfrac{h}{3}[/tex]Where,r = radius of the base circle,h = height of the cone.1. Cone with a diameter of 20 units and a height of 12 unitsHere,Radius = 20/2 = 10 unitsHeight = 12 units[tex]\text{Volume}_1=\pi \times 10^2\times \dfrac{12}{3}=400\pi[/tex]2. Cone with a diameter of 18 units and a height of 10 unitsHere,Radius = 18/2 = 9 unitsHeight = 10 units[tex]\text{Volume}_2=\pi \times 9^2\times \dfrac{10}{3}=270\pi[/tex]3. Cone with a radius of 10 units and a height of 9 unitsHere,Radius = 10 unitsHeight = 9 units[tex]\text{Volume}_3=\pi \times 10^2\times \dfrac{9}{3}=300\pi[/tex]4. Cone with a radius of 11 units and a height of 9 unitsHere,Radius = 11 unitsHeight = 9 units[tex]\text{Volume}_4=\pi \times 11^2\times \dfrac{9}{3}=363\pi[/tex]As,[tex]270\pi <300\pi <363\pi <400\pi[/tex][tex]\therefore \text{Volume}_2<\text{Volume}_3<\text{Volume}_4<\text{Volume}_1[/tex]