Advertisements
Advertisements
प्रश्न
If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere?
Advertisements
उत्तर
Let r be the radius of the sphere.
Surface area = 4πr2 and volume = `4/3pir^3`
According to the condition:
`4pir^2 = 4/3pir^3`
`=> r^3/r^2 = 4pi xx 3/(4pi)`
`=>` r = 3 cm
Diameter of sphere = 2 × 3 cm = 6 cm
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of radius 14 cm.
`["Assume "pi=22/7]`
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
Find the surface area of a sphere of diameter 14 cm.
Find the surface area of a sphere of diameter 21 cm.
The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :
- radii,
- surface areas.
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
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate: the number of cones recasted [π = 3.14]
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.
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 ______.
