The choices are not attached but we can solve the problem from the given information
Answer:
The expression can be used to find h is [tex]h=\frac{3V}{\pi r^{2}}[/tex]
The height of the cone is [tex]\frac{9}{\pi }[/tex] cm
Step-by-step explanation:
The formula of the volume of the cone is V = [tex]\frac{1}{3}[/tex] π r² h, where
Let us find the height of the cone from the formula of its volume
∵ V = [tex]\frac{1}{3}[/tex] π r² h
- Multiply both sides by 3
∴ 3 V = π r² h
- Divide both sides by π r²
∴ [tex]\frac{3V}{\pi r^{2}}=h[/tex]
- Switch the two sides
∴ [tex]h=\frac{3V}{\pi r^{2}}[/tex]
The expression can be used to find h is [tex]h=\frac{3V}{\pi r^{2}}[/tex]
∵ The radius of the cone is 7 cm
∴ r = 7
∵ The volume of the cone is 147 cm³
∴ V = 147
- Substitute them in the expression of the height to find it
∵ [tex]h=\frac{3(147)}{\pi (7)^{2}}[/tex]
∴ h = [tex]\frac{9}{\pi }[/tex] cm
The height of the cone is [tex]\frac{9}{\pi }[/tex] cm
