Advertisements
Advertisements
प्रश्न
If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is
विकल्प
12 cm
24 cm
30 cm
36 cm
उत्तर
Let r be the radius of single sphere.
Now,
The volume of single sphere = sum of volume of three spheres
`4/3pir^3 = 4/3pi(61)^3 + 4/3 pi(8)^3 + 4/3 pi(10)^3`
`4/3pir^3 = 4/3 pi(216 + 512 + 1000)`
`r^3 = 1728`
`r = 12 cm`
Hence, the diameter = 20 × r = 24 cm
APPEARS IN
संबंधित प्रश्न
A right triangle whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate.)
A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of the tent and the cost of the canvas at Rs 100 per square metre.
The inner diameter of a glass is 7 cm and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the figure. If the height of the glass is 16 cm, find the apparent capacity and the actual capacity of the glass.
A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied into a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel.
The surface areas of a sphere and a cube are equal. Find the ratio of their volumes.
Find the surface area of a sphere of radius 3.5 cm.
Tick the object which has more volume
A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square?
The surface areas of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 square centimetres. The volume of the solid, in cubic centimetres, is ______.
A running track has 2 semicircular ends of radius 63 m and two straight lengths. The perimeter of the track is 1000 m. Find each straight length.
