Answer:13.5 inches
Step-by-step explanation:
Here, the volume of a right circular cone varies jointly as the altitude and the square of the radius of the base
So our equation for volume becomes
V = c*h*r^2
where 'h' is altitude and 'r' is radius of base and 'c' is constant
Putting the value of V,h,r,
we get,
154 = c*12*3.5*3.5
c = 22/21
Now we have volume = 77 cu and radius of the base =7/3, so putting the values we get,
77 = 22/21*h*7/3*7/3
or, h= 13.5
Hope it helps!!!
Answer: 13.5 inches.
Step-by-step explanation:
Given : The volume of a right circular cone varies jointly as the altitude and the square of the radius of the base.
V α r² h , where r= radius and h = height.
i.e. V = k r² h (1), where c is the constant of proportionality.
When the volume of the cone is 154 cu. in. when its altitude is 12 in. and the radius of the base is [tex]3\dfrac{1}{2}\ in.[/tex] .
Put [tex]V= 154[/tex] , [tex]r =3\dfrac{1}{2}\ in. =\dfrac{7}{2}\ in.[/tex] and h = 12
in (1) , we get
[tex]154= k(\dfrac{7}{2})^2(12)[/tex]
[tex]154= k \dfrac{49}{4}(12)[/tex]
[tex]154= k (147)\\\\\Rightarrow\ k=\dfrac{154}{147}=\dfrac{22}{21}[/tex]
When the volume of the cone is 77 cu. in. and the radius of the base is [tex]2\dfrac{1}{3}\ in.[/tex]
Put V = 77 , [tex]r=2\dfrac{1}{3}=\dfrac{7}{3}\ in.[/tex] and [tex]k=\dfrac{22}{21}[/tex] in (1) , we get
[tex]77=(\dfrac{22}{21})(\dfrac{7}{3})^2h[/tex]
[tex]77=(\dfrac{22}{21})(\dfrac{49}{9})h[/tex]
[tex]77\times\dfrac{21}{22}\times\dfrac{9}{49}=h\\\\\Rightarrow\ h=\dfrac{27}{2}=13.5\ in.[/tex]
Hence, the altitude = 13.5 inches.
