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 number of cones recast. `("Take" pi =22/7)`
Advertisements
Solution
∴ R = 14 cm
Volume of sphere melted = `4/3 pi "R"^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 pi "r"^2"h"`
`= 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)`
= 128
RELATED QUESTIONS
Find the surface area of a sphere of radius 10.5 cm.
`["Assume "pi=22/7]`
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
Find the surface area of a sphere of diameter 21 cm.
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use ЁЭЬЛ = 3.14)
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 hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
Find the volume of a sphere, if its surface area is 154 sq.cm.
A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder .
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]
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown.
Calculate :
- the total surface area.
- the total volume of the solid and
- the density of the material if its total weight is 1.7 kg.
