Advertisements
Advertisements
Question
A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. Determine the internal diameter of the shell.
Solution
External radius of spherical shell
`r_1 = 18 /2 = 9 cm`
Let r2 be the internal radius of spherical shell.
Height of right circular cylinder h = 8 cm
& radius of right circular cylinder
`r = 12 /2 = 6 cm`
Clearly, volume of spherical shell = volume of right circular cylinder
`4/3 pi (r_1^3 - r_2^3 ) = pi r^2 h`
`4/3(9^3 - r_2^3) = (6)^2 xx 8`
`729 - r_3^2 = (36^9 xx 8 xx 3)/4`
`729 - r_2^3 = 216`
` r_2^3 = 513`
` r_2 = 3sqrt513`
` r_2 = 3(19)^(1/3) cm`
APPEARS IN
RELATED QUESTIONS
Find the total surface area of a cylinder if the radius of its base is 5 cm and height is 40 cm.
The diameter and length of a roller is 120 cm and 84 cm respectively. To level the ground, 200 rotations of the roller are required. Find the expenditure to level the ground at the rate of Rs. 10 per sq.m.
In the middle of a rectangular field measuring 30 m × 20 m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.
The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.
Water is flowing at the rate of 6 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 60 m long and 22 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.
If each edge of a cube is increased by 50%, the percentage increase in the surface area is
The diameter of a cylinder is 28 cm and its height is 20 cm. The total surface area of the cylinder is
The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is
Find the surface area of a sphere of radius 3.5 cm.
Tick the object which has more volume
