Advertisements
Advertisements
प्रश्न
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.
Advertisements
उत्तर
Radius of sphere = 3 cm
Radius of first ball = 1.5 cm
Radius of second ball = 2 cm
Radius of second ball = 2 cm
`=4/3pixx3^3 -(4/3pixx3^3/2+4/3pixx2^3)`
`=4/3pixx3xx3xx3 - (4/3pixx3/2xx3/2xx3/2+4/3pixx2xx2xx2)`
`=4pixx3xx3-(pixx(3xx3)/2 + 4/3pixx2xx2xx2)`
`=36pi - (pi9/2+32/3pi)`
`=((36xx6-9xx3-32xx2)/6)pi `
`=((216-27-64)/6)pi =(125pi)/6`
Therefore,
`4/3pir^3 = (125pi)/6`
`Or, r = root(3)((125xx3)/(4xx6)) = root(3)(125/8) = 5/2 = 2.5 "cm"`
APPEARS IN
संबंधित प्रश्न
A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs. 5 per 100 sq. cm. [Use π = 3.14]
If the total surface area of a solid hemisphere is 462 cm2 , find its volume.[Take π=22/7]
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. [Use `pi = 22/7`]
A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. [Use π = `22/7`]
Water in a canal, 5·4 m wide and 1·8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation?
A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively.The radii of the hemispherical and conical parts are the same as that of the cylindrical part.Find the surface area of the toy if the total height of the toy is 30 cm.
If the radii of circular ends of a bucket 24cm high are 5cm and 15cm. find surface area of
bucket?
A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 `3/7` cm3. The radii of its lower and upper circular ends are 8cm and 20cm. find the cost of metal sheet used in making container at rate of Rs 1.4 per cm2?
If r1 and r2 be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is \[\left( r_1^3 + r_2^3 \right)^\frac{1}{3}\].
A solid metal sphere of 6 cm diameter is melted and a circular sheet of thickness 1 cm is prepared. Determine the diameter of the sheet.
Two solid cones A and B are placed in a cylindrical tube as shown in fig .16.76. The ratio of their capacities are 2: 1 . Find the heights and capacities of the cones . Also, find the volume of the remaining portion of the cylinder.
A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be poured into cylindrical bottles of diameter 5 cm and height 6 cm each. Find the number of bottles required.
Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Find the volume of the resulting cuboid.
In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid points of sides AB, BC, CD and DA respectively. The area of the shaded portion is ______.
The shape of a gilli, in the gilli-danda game (see figure), is a combination of ______.
If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
Ramesh made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.
