Mathematics
A sphere is placed in an inverted hollow conical vessel of base radius 5 cm and vertical height 12 cm. If the highest point of the sphere is at the level of the base of the cone, find the radius of the sphere. Show that the volume of the sphere and the conical vessel are as 40 : 81.
Related Questions
A pool has a uniform circular cross section of radius 5 m and uniform depth 1.4 m. It is filled by a pipe which delivers water at the rate of 20 litres per sec. Calculate, in minutes, the time taken to fill the pool. If the pool is emptied in 42 min. by another cylindrical pipe through which water flows at 2 m per sec, calculate the radius of the pipe in cm.
The difference between the outer and the inner curved surface areas of a hollow cylinder, 14 cm long, is 88 sq. cm. Find the outer and the inner radii of the cylinder, given that the volume of metal used is 176 cu. cm.
The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its :
(i) radius
(ii) volume