Advertisements
Advertisements
Question
If the surface area of a sphere is 144π m2, then its volume (in m3) is
Options
288 π
316 π
300 π
188 π
Advertisements
Solution
In the given problem,
Surface area of a sphere = 144 π m2
So,
` 4 pi r^2 = 144 pi `
`r^2 = 144/4`
`r^2 = 36`
`r = sqrt(36)`
r = 6
Now, using the formula volume of the sphere, we get
`4/3 pi r^3 = 4/3 pi (6)^3`
` = 4/3 pi (216)`
`= 288 pi`
Therefore, volume of the sphere is `288 pi` .
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of radius 14 cm.
`["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]`
The surface area of a sphere is 5544 `cm^2`, find its diameter.
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 Rs. 4 per 100 `cm^2`
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.
A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid.
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
A sphere and a cube are of the same height. The ratio of their volumes is
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
If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is
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
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
Find the volume of a sphere, if its surface area is 154 sq.cm.
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
A conical tent is to accommodate 77 persons. Each person must have 16 m3 of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.
The cylinder of radius 12 cm have filled the 20 cm with water. One piece of iron drop in the stands of water goes up 6.75 cm. Find the radius of sphere piece.
A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm3 of ball bearings. Find the:
- maximum number of ball bearings that each box can have.
- mass of each box of ball bearings in kg.
(Use π = `22/7`)
