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arlik [135]
3 years ago
10

The volume of a right circular cone varies jointly as the altitude and the square of the radius of the base. If the volume of th

e cone is 154 cu. in. when its altitude is 12 in. and the radius of the base is 3 1/2 in., find the altitude when the volume of the cone is 77 cu. in. and the radius of the base is 2 1/3 in. Altitude = ? inches
Mathematics
2 answers:
Tresset [83]3 years ago
6 0

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!!!

irakobra [83]3 years ago
4 0

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 3\dfrac{1}{2}\ in. .

Put V= 154  ,  r =3\dfrac{1}{2}\ in. =\dfrac{7}{2}\ in. and h = 12

in (1) , we get

154= k(\dfrac{7}{2})^2(12)

154= k \dfrac{49}{4}(12)

154= k (147)\\\\\Rightarrow\ k=\dfrac{154}{147}=\dfrac{22}{21}

When the volume of the cone is 77 cu. in. and the radius of the base is 2\dfrac{1}{3}\ in.

Put V = 77 , r=2\dfrac{1}{3}=\dfrac{7}{3}\ in. and k=\dfrac{22}{21} in (1) , we get

77=(\dfrac{22}{21})(\dfrac{7}{3})^2h

77=(\dfrac{22}{21})(\dfrac{49}{9})h

77\times\dfrac{21}{22}\times\dfrac{9}{49}=h\\\\\Rightarrow\ h=\dfrac{27}{2}=13.5\ in.

Hence, the altitude = 13.5 inches.

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