Question

The volume of two cones of same base radius are 3600cm3 and 5040cm3 .find the ratio of heights

Answer 1

Answer:-

Given:

Two cones have same base radius.

And their volumes are 3600 cm³ and 5040 cm³.

Let the base radius of the cones be "r" cm and the heights of the cones be h1 and h2.

We know that,

Volume of a Cone = 1/3 * πr²h.

Hence,

Volume of first cone = 1/3*πr²h1 = 3600

→ πr²h1 = 3600*3

→ πr²h1 = 10800 -- equation (1)

Similarly,

→ 1/3*πr²h2 = 5040

→ πr²h2 = 5040*3

→ πr²h2 = 15120 -- equation (2)

Dividing equation (1) by (2) we get,

→ (πr²h1)/(πr²h2) = 10800/15120

π , r² are being cancelled in LHS.

→ h1/h2 = 10800/15120

→ h1/h2 = 5/7

Hence, the ratio of the heights of the cones is 5 : 7 or 7 : 5.

Answer 2

Answer:

Two cones have same base radius. And their volumes are 3600 cm3 and 5040 cm³. Let the base radius of the cones be "r" cm and the heights of the cones be h1 and h2. We know that, Volume of a Cone = 1/3 * TTr?h. Hence,

Volume of first cone = 1/3*ur?h1 = 3600 + Tr?h1 = 3600*3 + Trh( = (0800 -- equation (() Similarly, - 1/3*TTr?h2 = 5040 - Tur?h2 = 5040*3 + Trh2 = (5(20 -- equation (2) Dividing equation (1) by (2) we get, - (Tır?h1)/(r?h2) = 10800/15120.2 II, r are being cancelled in LHS. + h1/h2 = 10800/15120 → h(Uh2 = 5/9 Hence, the ratio of the heights of the cones is 5: 9 or 9 : 5.