Advertisements
Advertisements
प्रश्न
Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and recasted into a single solid sphere. Taking π = 3.1, find the surface area of the solid sphere formed.
Advertisements
उत्तर
Let radius of the larger sphere be ‘R’
Volume of single sphere
= Vol. of sphere 1 + Vol. of sphere 2 + Vol. of sphere 3
`4/3piR^3 = 4/3pir_1^3 + 4/3pir_2^3 + 4/3pir_3^3`
`4/3piR^3 = 4/3pir6^3 + 4/3pir8^3 + 4/3pi10^3`
R3 = [63 + 83 + 103]
R3 = [216 + 512 + 1000]
R3 = 1728
R3 = 123
∴ R = 12
Surface area of the sphere
= 4πR2
= 4 × 3.1 × 122
= 4 × 3.1 × 12 × 12
= 1785.6 cm2
APPEARS IN
संबंधित प्रश्न
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.
Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed.
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?
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.
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
A hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
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 number of cones recast. `("Take" pi =22/7)`
From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: the volume of remaining solid
The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹ 0.14 per cm2
