The Total solution for NCERT class 6-12
A metallic sphere ofradius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm.Find the height of the cylinder.
Answer - 1 : -
It is given that radius of the sphere (R) =4.2 cm
Also, Radius of cylinder (r) = 6 cm
Now, let height of cylinder = h
It is given that the sphere is melted into acylinder.
So, Volume of Sphere = Volume of Cylinder
∴ (4/3)×π×R3 = π×r2×h.
h = 2.74 cm
Metallic spheres ofradii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solidsphere. Find the radius of the resulting sphere.
Answer - 2 : -
A 20 m deep wellwith diameter 7 m is dug and the earth from digging is evenly spread out toform a platform 22 m by 14 m. Find the height of the platform.
Answer - 3 : -
A well ofdiameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenlyall around it in the shape of a circular ring of width 4 m to form anembankment. Find the height of the embankment.
Answer - 4 : -
A container shapedlike a right circular cylinder having diameter 12 cm and height 15 cm is fullof ice cream.
Answer - 5 : - The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
How many silvercoins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form acuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?
Answer - 6 : -
A cylindricalbucket, 32 cm high and with radius of base 18 cm, is filled with sand. Thisbucket is emptied on the ground and a conical heap of sand is formed. If theheight of the conical heap is 24 cm, find the radius and slant height of theheap.
Answer - 7 : -
Answer - 8 : -
A farmer connects apipe of internal diameter 20 cm from a canal into a cylindrical tank in herfield, which is 10 m in diameter and 2 m deep. If water flows through the pipeat the rate of 3 km/h, in how much time will the tank be filled?
Answer - 9 : -
Consider the following diagram-
Volume of water that flows in t minutes frompipe = t×0.5π m3
Radius (r2) of circular end ofcylindrical tank =10/2 = 5 m
Depth (h2) of cylindrical tank = 2m
Let the tank be filled completely in tminutes.
Volume of water filled in tank in t minutes isequal to the volume of water flowed in t minutes from the pipe.
Volume of water that flows in t minutes frompipe = Volume of water in tank
t×0.5π = π×r22×h2
Or, t = 100 minutes