Advertisements
Advertisements
प्रश्न
The surface area of a sphere is 2464 cm2, find its volume.
उत्तर
Surface area of the sphere = 2464 cm2
Let radius = r, then
4πr2 = 2464
`=> 4 xx 22/7 xx r^2 = 2464`
`=> r^2 = (2462 xx 7)/(4 xx 22) = 196`
`=>` r = 14 cm
Volume = `4/3pir^3`
∴ `4/3pir^3`
= `4/3 xx 22/7 xx 14 xx 14 xx 14`
= 11498.67 cm3
APPEARS IN
संबंधित प्रश्न
A right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate:
- the radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
The surface area of a sphere is 5544 `cm^2`, find its diameter.
Assuming the earth to be a sphere of radius 6370 km, how many square kilo metres is area
of the land, if three-fourth of the earth’s surface is covered by water?
A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base
of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100
`cm^2`.
The surface area of a solid sphere is increased by 12% without changing its shape. Find the percentage increase in its:
- radius
- volume
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.
Calculate:
- its volume,
- the surface area of the tunnel (excluding the floor) and
- its floor area.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
The total surface area of a hemisphere of radius r is
The ratio of the total surface area of a sphere and a hemisphere of same radius is
A sphere and a cube are of the same height. The ratio of their volumes is
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is
Find the radius of a sphere whose surface area is equal to the area of the circle of diameter 2.8 cm
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown.
Calculate :
- the total surface area.
- the total volume of the solid and
- the density of the material if its total weight is 1.7 kg.
A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.
A sphere cut out from a side of 7 cm cubes. Find the volume of this sphere?
