Advertisements
Advertisements
प्रश्न
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
उत्तर
Let edge of the cube = a
Volume of the cube = a × a × a = a3
The sphere, which exactly fits in the cube, has radius = `a/2`
Therefore, volume of sphere = `4/3pir^3`
= `4/3 xx 22/7 xx (a/2)^3`
= `4/3 xx 22/7 xx a^3/8`
= `11/21 a^3`
Volume of cube : Volume of sphere
= `a^3 : 11/21 a^3`
= `1 : 11/21`
= 21 : 11
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
Find the surface area of a sphere of radius 14 cm.
Find the surface area of a sphere of diameter 14 cm .
Find the surface area of a sphere of diameter 21 cm .
Find the surface area of a sphere of diameter 3.5 cm .
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.
Find the volume of a sphere whose surface area is 154 cm2.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
The model of a building is constructed with the scale factor 1 : 30.
(i) If the height of the model is 80 cm, find the actual height of the building in meters.
(ii) If the actual volume of a tank at the top of the building is 27m3, find the volume of the tank on the top of the model.
Find the volume of a sphere, if its surface area is 154 sq.cm.
Find the radius of the sphere whose surface area is equal to its volume .
A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.
The cylinder of radius 12 cm have filled the 20 cm with water. One piece of iron drop in the stands of water goes up 6.75 cm. Find the radius of sphere piece.
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.
