Question

For a fixed volume, the height, h cm, of a cone is inversely proportional to the square of the base rafius,r cm. Cine a has a base radius of 6 cm and a height of 5cm. The base radius of cone B is 3 cm and the height of cone C is 1.25 cm. If all the cones have the same volume, find the height of cone B

Answer 1

A/q h directly proportional to 1/r^2

h=k/r^2 {k = constant}

As per the question thrice have same volume which is

$1 \div 3\pi \: {r}^{2} \times h$

$1 \div 3 \times \pi \times {6}^{2} \times 5$

60π cm^2

r of cone B = 3 cm^2

h of cone B =k/3^2

volume of cone B = 60πcm^2

$60\pi = 1 \div 3\pi \times {3}^{2} \times k \div {3}^{2}$

$60 = k \div 3$

$k = 60 \times 3$

k= 180

h of B = k/3^2

h of B = 180/3×3

h of B = 20 cm

Answer 2

Answer:

Height of cone B = 10 cm

Base Radius of cone C = 37.5 cm

Step-by-step explanation:

Cone B

h=k/r        

5=k/6        

k=30

h=30/r

h=30/3

h=10cm radius

Cone C

h=k/r

r=h*k

r=1.25*30  

r=37.5 cm

This is correct answer