Question

By melting a solid cylindrical metal a few conical materials are to be made if three times the radius of cone is equal to twice the radius of the cone and the ratio of the height of the cylinder and cone is 4:3 find the number of cones which can be made

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The number of cones that can be made are 9.

Let the radius of cylinder be = R

Let the height of cylinder be = H

Let the radius of cone be = R

Let the height of cone be = H

Therefore, 3r = 2R And H ; h = 4 : 3 -- 1

= H/h = 4/3

= 3H = 4h --- 2

Let the required number of cones formed from the materials of the cylinder be = n

Thus, volume of the cylinder = sum of the volumes of n cones.

πR²H = n/3πr²h ( From equation 1 and 2)

= 3R²H = nr²h

n = 3R²H / r²h

n = 3 × 9r²/4 × 4h/3/ r²h

= 3 × 9 × 4 / 3 × 4

= 108 / 12

= 9

Therefore, 9 cones can be made.