Advertisements
Advertisements
प्रश्न
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :
- the radius of the solid sphere.
- the number of cones recast. [Take π = 3.14]
Advertisements
उत्तर
Total area of solid metallic sphere = 1256 cm2
i. Let radius of the sphere is r then
4πr2 = 1256
`=> 4 xx 22/7r^2 = 1256`
`=> r^2 = (1256 xx 7)/(4 xx 22)`
`=> r^2 = (157 xx 7)/11`
`=> r^2 = 1099/11`
`=> r = 1099/11`
`=> r = sqrt(99.909) = 9.995 cm`
`=>` r = 10 cm
ii. Volume of sphere = `4/3pir^3`
= `4/3 xx 22/7 xx 10 xx 10 xx 10`
= `88000/21 cm^3`
Volume of right circular cone = `1/3pir^2h`
= `1/3 xx 22/7 xx (2.5)^2 xx 8`
= `1100/21 cm^3`
Number of cones
= `88000/21 ÷ 1100/21`
= `88000/21 xx 21/1100`
= 80
संबंधित प्रश्न
Find the surface area of a sphere of diameter 3.5 m.
`["Assume "pi=22/7]`
Find the surface area of a sphere of radius 10.5 cm.
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`
The surface area of a sphere is 2464 cm2, find its volume.
A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
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.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
The ratio of the total surface area of a sphere and a hemisphere of same radius is
Find the radius of a sphere whose surface area is equal to the area of the circle of diameter 2.8 cm
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
