Advertisements
Advertisements
प्रश्न
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
उत्तर
We have,
the radii r1 = 6 cm, r2 = 8 and r3 = 10 cm
Let the radius of the resulting sphere be R.
As,
Volume of resulting sphere = Volume of three metallic spheres
`rArr 4/3piR^3 = 4/3pir_1^3 +4/3pir_2^3 +4/3pir_3^3`
`rArr 4/3piR^3 = 4/3pi(r_1^3 + r_2^3 + r_3^3)`
`rArr R^3 = r_1^3 + r_2^3 + r_3^3`
`rArr R^3 = 6^3 +8^3 + 10^3`
`rArr R^3 =216 + 512+1000`
`rArr R^3 =1728`
`rArr R = root(3)(1728)`
`rArr R= 12 "cm"`
So, the radius of the resulting sphere is 12 cm.
APPEARS IN
संबंधित प्रश्न
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform. [Use Π = 22/7]
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm? [Use π=22/7]
A farmer connects a pipe of internal diameter 20 cm form a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
A well of diameter 3 m is dug 14 m deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment ?
How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm .
Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape formed.
A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 cm and 9 cm respectively, then its slant height is
During conversion of a solid from one shape to another, the volume of the new shape will ______.
A cylindrical bucket, 32 cm high and 18 cm of radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box.
