Advertisements
Advertisements
Question
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 radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
Advertisements
Solution
i. Total surface area of the sphere = 4πr2, where r is the radius of the sphere.
Thus,
4πr2 = 2464 cm2
`=> 4 xx 22/7 xx r^2 = 2464`
`=>` r2 = 196
`=>` r = 14 cm
∴ R = 14 cm
ii. Volume of sphere melted = `4/3 piR^3`
= `4/3 xx pi xx 14 xx 14 xx 14`
Radius of each cone recasted = r = 3.5 cm
Height of each cone recasted = h = 7 cm
∴ Volume of each cone recasted = `1/3 pir^2h`
= `1/3 xx pi xx 3.5 xx 3.5 xx 7`
∴ Number of cones recasted
= `"Volume of sphere melted"/"Volume of each cone formed"`
= `(4/3 xx pi xx 14 xx 14 xx 14)/(1/3 xx pi xx 3.5 xx 3.5 xx 7)`
= `(4 xx 14 xx 14 xx 14)/(3.5 xx 3.5 xx 7)`
= 4 × 4 × 4 × 2
= 128
APPEARS IN
RELATED QUESTIONS
The diameter of the moon is approximately one fourth of the diameter of the earth. Find the
ratio of their surface areas.
If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere?
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, then the ratio of the volume of the sphere to the volume of the cube is
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
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 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 number of cones recasted [π = 3.14]
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 weight of the material drilled out if it weighs 7 gm per cm3.
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.
The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹ 0.14 per cm2
