Question

two cones A and B have their base radii in the ratio of 4:3 and their heights in the ratio 3:4 . The ratio of volume of cone A to that of cone B is ....??​

Answer 1

Answer:

Volume of Cone A: Volume of cone B= 4:3

Step-by-step explanation:

Step1)

Volume of cone A is Volume_A = 1/3 Pi  Radius_A x Radius_A x Height_A

Volume of cone B is Volume_B = 1/3 Pi  Radius-B x Radius_B x Height_B

Step2)

Volume_A / Volume_B=(1/3 Pi  Radius_A x Radius_A x Height_A) / 1/3 Pi  Radius-B x Radius_B x Height_B

Step3) Canceling out 1/3 and Pi in the above equation we have

Volume_A / Volume_B = (Radius_A x Radius_A x Height_A)/(Radius-B x Radius_B x Height_B)

Step3)

The above equation can be written as

Volume_A / Volume_B =(Radius_A/Radius_B) x (Radius_A/Radius_B) x ( Height_A / Height_B)

Step4)

In the question its given that :

Radius_A : Radius_B = 4:3

Height_A : Height_B= 3:4

We will replace these ratios in the above equation:

Volume_A/Volume_B= (4/3) x (4/3) x(3/4) =4/3 (Canceling out (4/3) x(3/4)