Advertisements
Advertisements
Question
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
Options
100 π
75 π
60 π
50 π
Advertisements
Solution
In the given problem, Let the radius of smaller spherical balls which can be made from a bigger ball be xunits.
Here,
The radius of the bigger ball (r1) = 10 cm
The radius of the smaller ball (r2) = x cm
The number of smaller balls = 8
So, volume of the big ball is equal to the volume of 8 small balls.
Volume of the big balls = volume of the 8 small balls
`(4/3)pi r_1^3 = 8 (4/3) pi x^3`
`(4/3) pi (10)^3 =8 (4/3) pi x^3`
`(10)^3 = 8 x^3`
`x^3 = 1000/8`
Further, solving for x, we get,
`x=3sqrt(1000/8) `
`x = 10/2`
x = 5
Now, surface area of a small ball of radius 5 cm = `4 pi r^2`
`= 4 pi(5)^2`
`= 100 pi`
Therefore, the surface area of the small spherical ball is `100 pi`.
APPEARS IN
RELATED QUESTIONS
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.
A model of a ship is made to a scale 1: 300
1) The length of the model of the ship is 2 m. Calculate the lengths of the ship.
2) The area of the deck ship is 180,000 m2. Calculate the area of the deck of the model.
3) The volume of the model in 6.5 m3. Calculate the volume of the ship.
Find the surface area of a sphere of radius 5.6 cm.
The surface area of a sphere is 5544 `cm^2`, find its diameter.
A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base
of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100
`cm^2`.
The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :
- radii,
- surface areas.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.
The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.
Calculate:
- its volume,
- the surface area of the tunnel (excluding the floor) and
- its floor area.
If the surface area of a sphere is 144π m2, then its volume (in m3) is
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
Find the radius of the sphere whose surface area is equal to its volume .
A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.
The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
The total surface area of a hemisphere is how many times the square of its radius
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 ______.
