Q. 16

A. 64:27

B. 16:9

C. 4:3

D. 16

Answer :

Given: Surface area ratio of two Spheres is: 16:9

Volume of the Sphere is: × π × r^{3} (where r is radius of sphere)

Surface area of the sphere is: 4 × π × r^{2} (where r is radius of sphere)

Let S_{1} and S_{2} be two different spheres.

(Surface area of) S_{1}: (Surface area of) S_{2} = 16:9

4 × π × (r_{1})^{2}: 4 × π × (r_{2})^{2} = 16:9 (here r_{1} and r_{2} are the radii of S_{1} and S_{2} respectively)

(r_{1})^{2}: (r_{2})^{2} = 16:9

r_{1}: r_{2} = √16:√9

r_{1}: r_{2} = 4:3

Now,

Let V_{1} and V_{2} be the volumes of the spheres S_{1} and S_{2} respectively.

∴ V_{1}:V_{2} = × π × (r_{1})^{3}: × π × (r_{2})^{3} (here r_{1} and r_{2} are the radii of S_{1} and S_{2} respectively)

⇒ V_{1}:V_{2} = (r_{1})^{3}: (r_{2})^{3}

⇒ V_{1}:V_{2} = (4)^{3}: (3)^{3}

⇒ V_{1}:V_{2} = 64:27

∴ The ratios of the volumes is: 64:27

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

RELATED QUESTIONS :

The radii of the base of a cylinder and a cone are in the ratio 3:4. If they have their height in the ratio 2:3, the ratio between their volumes is:

RS Aggarwal - MathematicsThe total surface area of a cube is 864 cm^{2}. Its volume is

The height of a cylinder is 14 cm and its curved surface area is 264 cm^{2}. The volume of the cylinder is

The radii of two cylinders are in the ratio 2:3 and their height in the ratio 5 : 3. The ratio of their volume is

RS Aggarwal - MathematicsA funnel is the combination of

RS Aggarwal - Mathematics

In a right circular cone, the cross section made by a plane parallel to the base is a

RS Aggarwal - MathematicsA cylindrical pencil sharpened at one edge is the combination of

RS Aggarwal - Mathematicsa right cylindrical vessel is full of water. How many right cones having the same radius and height as those of the right cylinder will be needed to store that water?

RS Aggarwal - MathematicsThe surface areas of two sphere are in the ratio of 4:25. Find the ratio of their volumes.

RS Aggarwal - Mathematics