Answer:
A) The exact value of the volume of the cone is 96 π meters³
B) The approximated value of the volume of the cone is 301.6 meters³
Step-by-step explanation:
The formula of the volume of a cone is V = [tex]\frac{1}{3}[/tex] π r² h, where
- r is the radius of its base
- h is its height
The figure is a cone with radius 6 meters and height 8 meters
A)
∵ The shape is a cone
∴ The formula of its volume is V = [tex]\frac{1}{3}[/tex] π r² h
∵ Its radius = 6 meters
∴ r = 6
∵ Its height = 8 meters
∴ h = 8 meters
- Substitute the values of r and h in the formula above
∴ V = [tex]\frac{1}{3}[/tex] π (6)² (8)
∴ V = 96 π meters³
The exact value of the volume of the cone is 96 π meters³
B)
To find the approximated value put the value of π
∴ The formula of its volume is V = [tex]\frac{1}{3}[/tex] π r² h
∵ Its radius = 6 meters
∴ r = 6
∵ Its height = 8 meters
∴ h = 8 meters
∵ π ≅ 3.141592654
- Substitute the values of π, r and h in the formula above
∴ V = [tex]\frac{1}{3}[/tex] (3.141592654) (6)² (8)
∴ V = 301.5928947 meters³
- Round it to the nearest tenth
∴ V = 301.6 meters³
The approximated value of the volume of the cone is 301.6 meters³
