Advertisements
Advertisements
Question
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
Options
27 \[\pi\] cm3
36 \[\pi\] cm3
108 \[\pi\] cm3
12 \[\pi\] cm3
Advertisements
Solution
In the given problem, the largest sphere is carved out of a cube and we have to find the volume of the sphere.
Side of a cube = 6 cm
So, for the largest sphere in a cube, the diameter of the sphere will be equal to side of the cube.
Therefore, diameter of the sphere = 6 cm
Radius of the sphere = 3 cm
Now, the volume of the sphere = `(4/3)pi r^3`
`=(4/3) pi (3)^3 `
= 36 π
Therefore, the volume of the largest sphere inside the given cube is 36 π .
APPEARS IN
RELATED QUESTIONS
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm2.
`["Assume "pi=22/7]`
A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
`["Assume "pi = 22/7]`
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.
A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.
What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
The model of a building is constructed with the scale factor 1 : 30.
(i) If the height of the model is 80 cm, find the actual height of the building in meters.
(ii) If the actual volume of a tank at the top of the building is 27m3, find the volume of the tank on the top of the model.
Find the surface area and volume of sphere of the following radius. (π = 3.14)
4 cm
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
9 cm
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre.
A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere .
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find volume of material of the vessel.
The volume of a sphere is 905 1/7 cm3, find its diameter.
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 ______.
