Two cones have their heights in the ratio 1 : 3 and the radii of their bases are in the ratio 3 : 1, then find the ratio of their volumes?

Question

Answer

The ratio of heights of two cones=1:3--( given)--(1).
ratio of radii of their base=3:1,---(2).{ given}
To find--> ratio of their volumes=?,
Volume of cone I/Volume of cone II=
1/3Πr1^2h1/1/3Πr2^2h2,
=r1^2h1/r2^2h2,
=(3/1)^2×(1/3),( from (1).and (2).)
=3:1

Answer

Let Height asCone1:(h1=X)Cone2:(h2=3X)Let Radius asCone1:(r1=3y)Cone2:(r2=y)Now Ratio={(Vol.of cone1)/(Vol.of Cone2)}={1/3 pie (r1)^2 (h1)}/ {1/3 Pie (r2)^2 (h2)}={(3y)^2 (X)} / {(Y)^2 (3X)}={9X(y^2)}/3X(y^2)}=3:1

Answer

Apply the formula of cylinder in both the cases and then divided ........ volume of case 1÷ volume of case 2 ............then we will get 3:1

Answer

3:1

Answer

3:1

Answer

Let h1 be xthen h2 =3xvolume of cylinder1=pie*(3r)square*xvolume of cylinder2=pie*rsquare*3xv1:v2=v1/v2=3/1=3:1

Answer

Explanation:

Given:
- The ratio of the heights of the cones is 1:3.
- The ratio of the radii of their bases is 3:1.

We need to find the ratio of their volumes.

Step 1: Understanding the concept

To find the ratio of the volumes of the cones, we need to understand the formula for the volume of a cone.

The volume of a cone can be calculated using the formula:
Volume = (1/3) * π * r^2 * h

Where:
- π is a constant (approximately 3.14)
- r is the radius of the base of the cone
- h is the height of the cone

Step 2: Finding the ratio of the volumes

Let's assume the height of the first cone is h1 and the radius of its base is r1.
Similarly, let's assume the height of the second cone is h2 and the radius of its base is r2.

Given that the heights of the cones are in the ratio 1:3, we can write:
h1/h2 = 1/3

Given that the radii of the bases are in the ratio 3:1, we can write:
r1/r2 = 3/1

Step 3: Applying the ratios to find the volumes

Let's assume the volume of the first cone is V1, and the volume of the second cone is V2.

Using the formula for the volume of a cone, we can write:
V1 = (1/3) * π * r1^2 * h1
V2 = (1/3) * π * r2^2 * h2

Step 4: Finding the ratio of the volumes

To find the ratio of the volumes, we divide V1 by V2:

V1/V2 = [(1/3) * π * r1^2 * h1] / [(1/3) * π * r2^2 * h2]

We can cancel out the common terms:
V1/V2 = (r1^2 * h1) / (r2^2 * h2)

Substituting the given ratios:
V1/V2 = (3^2 * 1) / (1^2 * 3) = 9/3 = 3/1

Step 5: Final answer

Therefore, the ratio of the volumes of the two cones is 3:1.

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