If r is the radius, S the surface area and V the volume of a spherical bubble, prove that
(i) `(dV)/(dt)=4pir^(2)(dr)/(dt)`

If r is the radius, S the surface area and V the volume of a spherical bubble, prove that (ii) (dV)/(dS) oo r

If S be the surface area of V be the volume of a sphere of radius r. Then (dv)/(dt) = (r)/(k) (ds)/(dt) . Value of k is

The total surface area of a hemisphere of radius r is pir^2 (b) 2pir^2 (c) 3pir^2 (d) 4pir^2

If r is the radius and h is height of the cylinder the volume will be (a) 1/3pi^2h (b) pir^2h (c) 2pir\ (h+r) (d) 2pir h

Which of the following is the ratio of the surface area of the sphere with radius r to its volume?

If r and T are radius and surface tension of a spherical soap bubble respectively then find the charge needed to double the radius of bubble.

A spheres has a volume of 36pi . What is the surface area of the sphere? (The surface area of a sphere is given by the formula A=4pir^(2) )

The volume of a sphere is given by V=4/3 piR^(3) where R is the radius of the radius of the sphere. Find the change in volume of the sphere as the radius is increased from 10.0 cm to 10.1 cm . Assume that the rate does not appreciably change between R=10.0 cm to R=10.1 cm

If the radius and surface tension of a spherical soap bubble be r and T respectively. Find the charge uniformly distributed over the outer surface of the bubble, is required to double its radius. (Given that atmospheric pressure is P_(0) and inside temperature of the bubble during expansion remains constant.)

Two soap bubbles are stuck together with an intermediate film separating them. Compute the radius of curvature of this film given that the radii of the bubbles in this arrangement are r_(1) and r_(2) respectively. If r_(1) gt r_(2) state clearly which way the intermediate film will bulge. For the case when r_(1)=r_(2)=2cm calculate he radius of the bubble formed by bursting the intermediate film. The volume of a spherical dome of radius R and height h is pib^(2)(3R-b)//3 .